1
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Zhang X, Hui TC, Ristenpart WD, Miller GH. Theoretical velocity of an object frictionally coupled to a two-mode vibrating plate. Phys Rev E 2024; 110:024212. [PMID: 39294964 DOI: 10.1103/physreve.110.024212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2024] [Accepted: 08/01/2024] [Indexed: 09/21/2024]
Abstract
Net velocity has been demonstrated for objects frictionally coupled to a flat plate that oscillates periodically in-plane with two frequencies, provided plate displacement is nonantiperiodic: the ratio of frequencies γ cannot be the ratio of two odd integers. We give a mathematical derivation of the experimentally determined dependence of mean velocity on the relative amplitudes of the two frequency modes, and the phase lag between the modes, when γ=2, and when the magnitude of plate acceleration is much larger than the magnitude of acceleration by static friction. The approach uses an analysis of the symmetry properties of the roots of trigonometric polynomials, without explicit determination of those roots. The behavior when γ=1/2, and specific phase lags that inhibit net velocity for general γ, are also determined.
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2
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Hashemi A, Gilman ET, Khair AS. A multiple-timing analysis of temporal ratcheting. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2024; 47:28. [PMID: 38676815 PMCID: PMC11055766 DOI: 10.1140/epje/s10189-024-00421-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2024] [Accepted: 04/04/2024] [Indexed: 04/29/2024]
Abstract
We develop a two-timing perturbation analysis to provide quantitative insights on the existence of temporal ratchets in an exemplary system of a particle moving in a tank of fluid in response to an external vibration of the tank. We consider two-mode vibrations with angular frequencies ω and α ω , where α is a rational number. If α is a ratio of odd and even integers (e.g.,2 1 , 3 2 , 4 3 ), the system yields a net response: here, a nonzero time-average particle velocity. Our first-order perturbation solution predicts the existence of temporal ratchets for α = 2 . Furthermore, we demonstrate, for a reduced model, that the temporal ratcheting effect for α = 3 2 and4 3 appears at the third-order perturbation solution. More importantly, we find closed-form formulas for the magnitude and direction of the induced net velocities for these α values. On a broader scale, our methodology offers a new mathematical approach to study the complicated nature of temporal ratchets in physical systems.
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Affiliation(s)
- Aref Hashemi
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA.
- Courant Institute, New York University, New York, NY, USA.
| | - Edward T Gilman
- Department of Mathematics, Rice University, Houston, TX, USA
| | - Aditya S Khair
- Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA
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3
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Hui TC, Zhang X, Adiga D, Miller GH, Ristenpart WD. Vibrational manipulation of dry granular materials in lab-on-a-chip devices. LAB ON A CHIP 2024. [PMID: 38275165 DOI: 10.1039/d3lc00722g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/27/2024]
Abstract
We present vibrational techniques to pump, mix, and separate dry granular materials using multifrequency vibrations applied to a solid substrate with a standard audio system. The direction and velocity of the granular flow are tuned by modulating the sign and amplitude, respectively, of the vibratory waveform, with typical pumping velocities of centimeters per second. Different granular materials are mixed by combining them at Y-shaped junctions, and mixtures of granules with different friction coefficients are separated along straight channels by judicious choice of the vibratory waveform. We demonstrate that the observed velocities accord with a theory valid for sufficiently large or fast vibrations, and we discuss the implications for using vibrational manipulation in conjunction with established microfluidic technologies to combine liquid and dry solid handling operations at sub-millimeter length scales.
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Affiliation(s)
- Timothy C Hui
- Dept. of Chemical Engineering, University of California Davis, One Shields Ave., Davis, CA 95616, USA.
| | - Xiaolin Zhang
- Dept. of Chemical Engineering, University of California Davis, One Shields Ave., Davis, CA 95616, USA.
| | - Dhruva Adiga
- Dept. of Chemical Engineering, University of California Davis, One Shields Ave., Davis, CA 95616, USA.
| | - Gregory H Miller
- Dept. of Chemical Engineering, University of California Davis, One Shields Ave., Davis, CA 95616, USA.
| | - William D Ristenpart
- Dept. of Chemical Engineering, University of California Davis, One Shields Ave., Davis, CA 95616, USA.
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4
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Dupont N, Gabardos L, Arrouas F, Ombredane N, Billy J, Peaudecerf B, Guéry-Odelin D. Hamiltonian Ratchet for Matter-Wave Transport. PHYSICAL REVIEW LETTERS 2023; 131:133401. [PMID: 37832021 DOI: 10.1103/physrevlett.131.133401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2023] [Revised: 07/26/2023] [Accepted: 08/15/2023] [Indexed: 10/15/2023]
Abstract
We report on the design of a Hamiltonian ratchet exploiting periodically at rest integrable trajectories in the phase space of a modulated periodic potential, leading to the linear nondiffusive transport of particles. Using Bose-Einstein condensates in a modulated one-dimensional optical lattice, we make the first observations of this spatial ratchet, which provides way to coherently transport matter waves with possible applications in quantum technologies. In the semiclassical regime, the quantum transport strongly depends on the effective Planck constant due to Floquet state mixing. We also demonstrate the interest of quantum optimal control for efficient initial state preparation into the transporting Floquet states to enhance the transport periodicity.
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Affiliation(s)
- N Dupont
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, UT3, Université de Toulouse, CNRS, 118 Route de Narbonne, 31062 Toulouse CEDEX 09, France
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
| | - L Gabardos
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, UT3, Université de Toulouse, CNRS, 118 Route de Narbonne, 31062 Toulouse CEDEX 09, France
| | - F Arrouas
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, UT3, Université de Toulouse, CNRS, 118 Route de Narbonne, 31062 Toulouse CEDEX 09, France
| | - N Ombredane
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, UT3, Université de Toulouse, CNRS, 118 Route de Narbonne, 31062 Toulouse CEDEX 09, France
| | - J Billy
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, UT3, Université de Toulouse, CNRS, 118 Route de Narbonne, 31062 Toulouse CEDEX 09, France
| | - B Peaudecerf
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, UT3, Université de Toulouse, CNRS, 118 Route de Narbonne, 31062 Toulouse CEDEX 09, France
| | - D Guéry-Odelin
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, UT3, Université de Toulouse, CNRS, 118 Route de Narbonne, 31062 Toulouse CEDEX 09, France
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5
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Saha AK, Ray DS, Deb B. Phase diffusion and fluctuations in a dissipative Bose-Josephson junction. Phys Rev E 2023; 107:034141. [PMID: 37073026 DOI: 10.1103/physreve.107.034141] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Accepted: 03/16/2023] [Indexed: 04/20/2023]
Abstract
We analyze the phase diffusion, quantum fluctuations and their spectral features of a one-dimensional Bose-Josephson junction (BJJ) nonlinearly coupled to a bosonic heat bath. The phase diffusion is considered by taking into account of random modulations of the BJJ modes causing a phase loss of initial coherence between the ground and excited states, whereby the frequency modulation is incorporated in the system-reservoir Hamiltonian by an interaction term linear in bath operators but nonlinear in system (BJJ) operators. We examine the dependence of the phase diffusion coefficient on the on-site interaction and temperature in the zero- and π-phase modes and demonstrate its phase transition-like behavior between the Josephson oscillation and the macroscopic quantum self-trapping (MQST) regimes in the π-phase mode. Based on the thermal canonical Wigner distribution, which is the equilibrium solution of the associated quantum Langevin equation for phase, coherence factor is calculated to study phase diffusion for the zero- and π-phase modes. We investigate the quantum fluctuations of the relative phase and population imbalance in terms of fluctuation spectra which capture an interesting shift in Josephson frequency induced by frequency fluctuation due to nonlinear system-reservoir coupling, as well as the on-site interaction-induced splitting in the weak dissipative regime.
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Affiliation(s)
- Abhik Kumar Saha
- School of Physical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Deb Shankar Ray
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Bimalendu Deb
- School of Physical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
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6
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Cubero D. Brillouin propagation modes of cold atoms undergoing Sisyphus cooling. Phys Rev E 2023; 107:034102. [PMID: 37072942 DOI: 10.1103/physreve.107.034102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2022] [Accepted: 02/13/2023] [Indexed: 04/20/2023]
Abstract
An exact expression for the average velocity of cold atoms in a driven, dissipative optical lattice in terms of the amplitudes of atomic density waves is derived from semiclassical equations for the phase space densities of the Zeeman ground-state sublevels. The calculations are for a J_{g}=1/2→J_{e}=3/2 transition, as it is customary in theoretical studies of Sisyphus cooling. While the driver, an additional beam of small amplitude, sets the atoms into directed motion, the new expression permits the quantification of the contribution to the atomic motion of a specific atomic wave, revealing unexpected counterpropagating contributions from many modes. Additionally, the method is shown to provide the generic threshold for the transition into the regime of infinite density, regardless of the details, or even the presence, of driving.
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Affiliation(s)
- David Cubero
- Departamento de Física Aplicada I, Escuela Politécnica Superior, Universidad de Sevilla, Calle Virgen de África 7, 41011 Sevilla, Spain
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7
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Spiechowicz J, Marchenko IG, Hänggi P, Łuczka J. Diffusion Coefficient of a Brownian Particle in Equilibrium and Nonequilibrium: Einstein Model and Beyond. ENTROPY (BASEL, SWITZERLAND) 2022; 25:42. [PMID: 36673183 PMCID: PMC9857877 DOI: 10.3390/e25010042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Revised: 12/21/2022] [Accepted: 12/21/2022] [Indexed: 06/17/2023]
Abstract
The diffusion of small particles is omnipresent in many processes occurring in nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow our survey to the case of the diffusion coefficient for a Brownian particle that can be modeled in the framework of Langevin dynamics. Our main focus centers on the temperature dependence of the diffusion coefficient for several fundamental models of diverse physical systems. Starting out with diffusion in equilibrium for which the Einstein theory holds, we consider a number of physical situations outside of free Brownian motion and end by surveying nonequilibrium diffusion for a time-periodically driven Brownian particle dwelling randomly in a periodic potential. For this latter situation the diffusion coefficient exhibits an intriguingly non-monotonic dependence on temperature.
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Affiliation(s)
- Jakub Spiechowicz
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
| | - Ivan G. Marchenko
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
- Kharkiv Institute of Physics and Technology, 61108 Kharkiv, Ukraine
- Education and Research Institute of Computer Physics and Energy, Karazin Kharkiv National University, 61022 Kharkiv, Ukraine
| | - Peter Hänggi
- Institute of Physics, University of Augsburg, 86135 Augsburg, Germany
- Max-Planck Institute for Physics of Complex Systems, 01187 Dresden, Germany
| | - Jerzy Łuczka
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
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8
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Minguzzi J, Zhu Z, Sandholzer K, Walter AS, Viebahn K, Esslinger T. Topological Pumping in a Floquet-Bloch Band. PHYSICAL REVIEW LETTERS 2022; 129:053201. [PMID: 35960575 DOI: 10.1103/physrevlett.129.053201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 06/21/2022] [Indexed: 06/15/2023]
Abstract
Constructing new topological materials is of vital interest for the development of robust quantum applications. However, engineering such materials often causes technological overhead, such as large magnetic fields, spin-orbit coupling, or dynamical superlattice potentials. Simplifying the experimental requirements has been addressed on a conceptual level-by proposing to combine simple lattice structures with Floquet engineering-but there has been no experimental implementation. Here, we demonstrate topological pumping in a Floquet-Bloch band using a plain sinusoidal lattice potential and two-tone driving with frequencies ω and 2ω. We adiabatically prepare a near-insulating Floquet band of ultracold fermions via a frequency chirp, which avoids gap closings en route from trivial to topological bands. Subsequently, we induce topological pumping by slowly cycling the amplitude and the phase of the 2ω drive. Our system is well described by an effective Shockley model, establishing a novel paradigm to engineer topological matter from simple underlying lattice geometries. This approach could enable the application of quantized pumping in metrology, following recent experimental advances on two-frequency driving in real materials.
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Affiliation(s)
- Joaquín Minguzzi
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | - Zijie Zhu
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | - Kilian Sandholzer
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | | | - Konrad Viebahn
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | - Tilman Esslinger
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
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9
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Hashemi A, Tahernia M, Hui TC, Ristenpart WD, Miller GH. Net motion induced by nonantiperiodic vibratory or electrophoretic excitations with zero time average. Phys Rev E 2022; 105:065001. [PMID: 35854501 DOI: 10.1103/physreve.105.065001] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Accepted: 05/26/2022] [Indexed: 06/15/2023]
Abstract
It is well established that application of an oscillatory excitation with zero time-average but temporal asymmetry can yield net drift. To date this temporal symmetry breaking and net drift has been explored primarily in the context of point particles, nonlinear optics, and quantum systems. Here, we present two new experimental systems where the impact of temporally asymmetric force excitations can be readily observed with mechanical motion of macroscopic objects: (1) solid centimeter-scale objects placed on a uniform flat surface made to vibrate laterally, and (2) charged colloidal particles in water placed between parallel electrodes with an applied oscillatory electric potential. In both cases, net motion is observed both experimentally and numerically with nonantiperiodic, two-mode, sinusoids where the frequency modes are the ratio of odd and even numbers (e.g., 2Hz and 3Hz). The observed direction of motion is always the same for the same applied waveform, and is readily reversed by changing the sign of the applied waveform, for example, by swapping which electrode is powered and grounded. We extend these results to other nonlinear mechanical systems, and we discuss the implications for facile control of object motion using tunable periodic driving forces.
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Affiliation(s)
- Aref Hashemi
- Courant Institute, New York University, New York, New York, USA
| | - Mehrdad Tahernia
- Department of Information Engineering, The Chinese University of Hong Kong, China
| | - Timothy C Hui
- Department of Chemical Engineering, University of California Davis, Davis, California, USA
| | - William D Ristenpart
- Department of Chemical Engineering, University of California Davis, Davis, California, USA
| | - Gregory H Miller
- Department of Chemical Engineering, University of California Davis, Davis, California, USA
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10
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Chacón R, Martínez PJ. Directed ratchet transport of cold atoms and fluxons driven by biharmonic fields: A unified view. Phys Rev E 2021; 104:014120. [PMID: 34412244 DOI: 10.1103/physreve.104.014120] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2021] [Accepted: 06/21/2021] [Indexed: 11/07/2022]
Abstract
This paper discusses two retrodictions of the theory of ratchet universality which explain previous experimental results concerning directed ratchet transport of cold atoms in dissipative optical lattices in one case and of fluxons in uniform annular Josephson junctions in the other, both driven by biharmonic fields. It has to be emphasized that these retrodictions are in sharp contrast with the current standard explanation of such experimental results, and they offer optimal control of the ratchetlike motion of such entities. New experimental proposals with cold atoms and fluxons are discussed, providing additional tests for novel predictions from ratchet universality.
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Affiliation(s)
- Ricardo Chacón
- Departamento de Física Aplicada, E.I.I., Universidad de Extremadura, Apartado Postal 382, E-06006 Badajoz, Spain and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain
| | - Pedro J Martínez
- Departamento de Física Aplicada, E.I.N.A., Universidad de Zaragoza, E-50018 Zaragoza, Spain and Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, E-50009 Zaragoza, Spain
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11
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Martínez PJ, Chacón R. Ratchet universality in coupled dissipative oscillators without external bias. Phys Rev E 2021; 104:024224. [PMID: 34525664 DOI: 10.1103/physreve.104.024224] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 08/16/2021] [Indexed: 06/13/2023]
Abstract
Directed ratchet transport is generally observed in nonautonomous systems as a result of the interplay of nonlinearity, symmetry breaking, and nonequilibrium fluctuations. Here we demonstrate that ratchet dynamics can appear in significant transporting degrees of freedom of dissipative coupled systems without external bias due to unidirectional coupling of oscillatory degrees of freedom (which are also nonbiasing in any direction), while optimal enhancement of directed ratchet transport occurs when the initial conditions and parameters of such ratcheting degrees of freedom are suitably chosen as predicted by the theory of ratchet universality. The simple case of linear oscillatory degrees of freedom is discussed in detail, and numerical experiments are described which confirm all the theoretical predictions, including the dependence of current (velocity) reversals on the initial conditions and the ratcheting degrees-of-freedom parameters. This autonomous ratchet scenario could be exploited technologically, for instance, in the context of noncontact, rack-and-pinion type, nanoscale setups with coupling from the lateral Casimir force, and is relevant for studies of molecular motors in the biological realm.
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Affiliation(s)
- Pedro J Martínez
- Instituto de Nanociencia y Materiales de Aragón, CSIC-Universidad de Zaragoza, E-50009 Zaragoza, Spain
- Departamento de Física Aplicada, E.I.N.A., Universidad de Zaragoza, E-50018 Zaragoza, Spain
| | - Ricardo Chacón
- Departamento de Física Aplicada, E.I.I., Universidad de Extremadura, Apartado Postal 382, E-06006 Badajoz, Spain
- Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain
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12
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Chacón R, Martínez PJ, Marcos JM, Aranda FJ, Martínez JA. Ratchet universality in the bidirectional escape from a symmetric potential well. Phys Rev E 2021; 103:022203. [PMID: 33736113 DOI: 10.1103/physreve.103.022203] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2020] [Accepted: 01/19/2021] [Indexed: 11/07/2022]
Abstract
The present work discusses symmetry-breaking-induced bidirectional escape from a symmetric metastable potential well by the application of zero-average periodic forces in the presence of dissipation. We characterized the interplay between heteroclinic instabilities leading to chaotic escape and breaking of a generalized parity symmetry leading to directed ratchet escape to an attractor either at ∞ or at -∞. Optimal enhancement of directed ratchet escape is found to occur when the wave form of the zero-average periodic force acting on the damped driven oscillator matches as closely as possible to a universal wave form, as predicted by the theory of ratchet universality. Specifically, the optimal approximation to the universal force triggers the almost complete destruction of the nonescaping basin for driving amplitudes which are systematically lower than those corresponding to a symmetric periodic force having the same period. We expect that this work could be potentially useful in the control of elementary dynamic processes characterized by multidirectional escape from a potential well, such as forced chaotic scattering and laser-induced dissociation of molecular systems, among others.
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Affiliation(s)
- R Chacón
- Departamento de Física Aplicada, Escuela de Ingenierías Industriales, Universidad de Extremadura, Apartado Postal 382, E-06006 Badajoz, Spain
- Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain
| | - P J Martínez
- Departamento de Física Aplicada, E.I.N.A., Universidad de Zaragoza, E-50018 Zaragoza, Spain and Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, E-50009 Zaragoza, Spain
| | - J M Marcos
- Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain
- Departamento de Física, Facultad de Ciencias, Universidad de Extremadura, E-06006 Badajoz, Spain
| | - F J Aranda
- Departamento de Ingeniería Eléctrica, Electrónica y Automática, Facultad de Ciencias, Universidad de Extremadura, E-06006 Badajoz, Spain
| | - J A Martínez
- Departamento de Ingeniería Eléctrica, Electrónica y Automática, Escuela de Ingenieros Industriales, Universidad de Castilla-La Mancha, E-02071 Albacete, Spain
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13
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Abstract
We demonstrate that directed transport of particles in a two dimensional driven lattice can be dynamically reversed multiple times by superimposing additional spatially localized lattices on top of a background lattice. The timescales of such current reversals can be flexibly controlled by adjusting the spatial locations of the superimposed lattices. The key principle behind the current reversals is the conversion of the particle dynamics from chaotic to ballistic, which allow the particles to explore regions of the underlying phase space which are inaccessible otherwise. Our results can be experimentally realized using cold atoms in driven optical lattices and allow for the control of transport of atomic ensembles in such setups.
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14
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Casado-Pascual J, Sánchez-Rey B, Quintero NR. Soliton ratchet induced by random transitions among symmetric sine-Gordon potentials. CHAOS (WOODBURY, N.Y.) 2019; 29:053119. [PMID: 31154783 DOI: 10.1063/1.5092797] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2019] [Accepted: 04/29/2019] [Indexed: 06/09/2023]
Abstract
The generation of net soliton motion induced by random transitions among N symmetric phase-shifted sine-Gordon potentials is investigated, in the absence of any external force and without any thermal noise. The phase shifts of the potentials and the damping coefficients depend on a stationary Markov process. Necessary conditions for the existence of transport are obtained by an exhaustive study of the symmetries of the stochastic system and of the soliton velocity. It is shown that transport is generated by unequal transfer rates among the phase-shifted potentials or by unequal friction coefficients or by a properly devised combination of potentials (N>2). Net motion and inversions of the currents, predicted by the symmetry analysis, are observed in simulations as well as in the solutions of a collective coordinate theory. A model with high efficient soliton motion is designed by using multistate phase-shifted potentials and by breaking the symmetries with unequal transfer rates.
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Affiliation(s)
- Jesús Casado-Pascual
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, 41080 Sevilla, Spain
| | - Bernardo Sánchez-Rey
- Departamento de Física Aplicada I, E.P.S., Universidad de Sevilla, Virgen de África 7, 41011 Sevilla, Spain
| | - Niurka R Quintero
- Departamento de Física Aplicada I, E.P.S., Universidad de Sevilla, Virgen de África 7, 41011 Sevilla, Spain
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15
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Słapik A, Łuczka J, Hänggi P, Spiechowicz J. Tunable Mass Separation via Negative Mobility. PHYSICAL REVIEW LETTERS 2019; 122:070602. [PMID: 30848611 DOI: 10.1103/physrevlett.122.070602] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2018] [Revised: 11/22/2018] [Indexed: 06/09/2023]
Abstract
A prerequisite for isolating diseased cells requires a mechanism for effective mass-based separation. This objective, however, is generally rather challenging because typically no valid correlation exists between the size of the particles and their mass value. We consider an inertial Brownian particle moving in a symmetric periodic potential and subjected to an externally applied unbiased harmonic driving in combination with a constant applied bias. In doing so, we identify a most efficient separation scheme which is based on the anomalous transport feature of negative mobility, meaning that the immersed particles move in the direction opposite to the acting bias. This work is the first of its kind in demonstrating a tunable separation mechanism in which the particle mass targeted for isolation is effectively controlled over a regime of nearly 2 orders of mass magnitude upon changing solely the frequency of the external harmonic driving. This approach may provide mass selectivity required in present and future separation of a diversity of nano- and microsized particles of either biological or synthetic origin.
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Affiliation(s)
- A Słapik
- Institute of Physics and Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów, Poland
| | - J Łuczka
- Institute of Physics and Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów, Poland
| | - P Hänggi
- Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany
- Nanosystems Initiative Munich, Schellingstraße 4, D-80799 München, Germany
| | - J Spiechowicz
- Institute of Physics and Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów, Poland
- Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany
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16
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Spiechowicz J, Łuczka J. SQUID ratchet: Statistics of transitions in dynamical localization. CHAOS (WOODBURY, N.Y.) 2019; 29:013105. [PMID: 30709158 DOI: 10.1063/1.5063335] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2018] [Accepted: 12/19/2018] [Indexed: 06/09/2023]
Abstract
We study occupation of certain regions of phase space of an asymmetric superconducting quantum interference device (SQUID) driven by thermal noise, subjected to an external ac current and threaded by a constant magnetic flux. Thermally activated transitions between the states which reflect three deterministic attractors are analyzed in the regime of the noise induced dynamical localization of the Josephson phase velocity, i.e., there is a temperature interval in which the conditional probability of the voltage to remain in one of the states is very close to one. Implications of this phenomenon on the dc voltage drop across the SQUID are discussed. We detect the emergence of the power law tails in a residence time probability distribution of the Josephson phase velocity and discuss the role of symmetry breaking in dynamical localization induced by thermal noise. This phenomenon illustrates how deterministic-like behavior may be extracted from randomness by stochasticity itself. It reveals another face of noise.
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Affiliation(s)
| | - Jerzy Łuczka
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
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17
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Chen R, Nie L, Chen C. Symmetry breaking: Abnormal transport induced by mass modulation. CHAOS (WOODBURY, N.Y.) 2018; 28:053115. [PMID: 29857649 DOI: 10.1063/1.5006955] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Here, we investigate transport of an inertial particle in a symmetric periodic potential and subjected to an external signal, such that mass of the particle is modulated sinusoidally. Our numerical results indicate that the mass modulation can induce abnormal transport in the system, whereas no current appears in the case of constant mass. In the absence of external bias, direction of mean velocity of the particle changes several times as amplitude and frequency of the mass modulation are varied, i.e., a multiple current reversals (CR) phenomenon. The multiple CRs result from temporal symmetry breaking of the system. In the presence of external bias, multiple absolute negative mobilities (ANM) take place in the system. Intrinsic physical mechanisms responsible for the occurrence of the multiple ANMs are analyzed in detail.
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Affiliation(s)
- Ruyin Chen
- Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
| | - Linru Nie
- Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
| | - Chongyang Chen
- Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
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18
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Mukhopadhyay AK, Xie T, Liebchen B, Schmelcher P. Dimensional coupling-induced current reversal in two-dimensional driven lattices. Phys Rev E 2018; 97:050202. [PMID: 29906956 DOI: 10.1103/physreve.97.050202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2018] [Indexed: 06/08/2023]
Abstract
We show that the direction of directed particle transport in a two-dimensional ac-driven lattice can be dynamically reversed by changing the structure of the lattice in the direction perpendicular to the applied driving force. These structural changes introduce dimensional coupling effects, the strength of which governs the timescale of the current reversals. The underlying mechanism is based on the fact that dimensional coupling allows the particles to explore regions of phase space which are inaccessible otherwise. The experimental realization for cold atoms in ac-driven optical lattices is discussed.
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Affiliation(s)
- Aritra K Mukhopadhyay
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Tianting Xie
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- College of Mathematics, Sichuan University, Chengdu 610065, China
| | - Benno Liebchen
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine Universität Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany
| | - Peter Schmelcher
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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19
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Wulf T, Okupnik A, Schmelcher P. Diffusion and transport in locally disordered driven lattices. CHAOS (WOODBURY, N.Y.) 2016; 26:093102. [PMID: 27781445 DOI: 10.1063/1.4961965] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density distribution which even increases towards larger positions is shown, thus yielding a highly non-Gaussian particle density evolution. As the key underlying mechanism, we identify the conversion between different components of the unperturbed systems mixed phase space which is induced by the disorder. Based on the introduction of individual conversion rates between chaotic and regular components, a theoretical model is developed which correctly predicts the scaling of the particle density. The effect of disorder on the transport properties is studied where a significant enhancement of the transport for cases of localized disorder is shown, thereby contrasting strongly the merely weak modification of the transport for global disorder.
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Affiliation(s)
- Thomas Wulf
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Alexander Okupnik
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Peter Schmelcher
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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20
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Ruyin C, Wanli P, Jianqiang Z, Linru N. Multiple absolute negative mobilities. CHAOS (WOODBURY, N.Y.) 2016; 26:093113. [PMID: 27781482 DOI: 10.1063/1.4961966] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In this paper, we investigate transport of an inertial particle in a spatially symmetric potential and subjected to two harmonic signals with different frequencies in both deterministic and stochastic cases. Numerical results indicate that: (i) In the deterministic case, the two harmonic signals can induce many (up to six) segments of negative slopes in the curve of mean velocity vs. external constant force, i.e., a multiple absolute negative mobilities (ANMs) effect. But the occurrence of the effect depends on their frequencies and amplitudes. (ii) For the stochastic case, the multiple ANMs relay on stable index and symmetry parameter of the Lévy noise. In the case of symmetric noise, appropriate stable index makes the multiple ANMs be the strongest. Our further investigations indicate that an indispensable condition for the multiple ANMs to occur in the system is the temporal symmetry breaking by one multiplicative periodic signal and one additive periodic signal.
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Affiliation(s)
- Chen Ruyin
- Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China
| | - Pan Wanli
- Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China
| | - Zhang Jianqiang
- Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China
| | - Nie Linru
- Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China
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21
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Spiechowicz J, Łuczka J, Hänggi P. Transient anomalous diffusion in periodic systems: ergodicity, symmetry breaking and velocity relaxation. Sci Rep 2016; 6:30948. [PMID: 27492219 PMCID: PMC4974640 DOI: 10.1038/srep30948] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2016] [Accepted: 07/11/2016] [Indexed: 11/18/2022] Open
Abstract
We study far from equilibrium transport of a periodically driven inertial Brownian particle moving in a periodic potential. As detected for a SQUID ratchet dynamics, the mean square deviation of the particle position from its average may involve three distinct intermediate, although extended diffusive regimes: initially as superdiffusion, followed by subdiffusion and finally, normal diffusion in the asymptotic long time limit. Even though these anomalies are transient effects, their lifetime can be many, many orders of magnitude longer than the characteristic time scale of the setup and turns out to be extraordinarily sensitive to the system parameters like temperature or the potential asymmetry. In the paper we reveal mechanisms of diffusion anomalies related to ergodicity of the system, symmetry breaking of the periodic potential and ultraslow relaxation of the particle velocity towards its steady state. Similar sequences of the diffusive behaviours could be detected in various systems including, among others, colloidal particles in random potentials, glass forming liquids and granular gases.
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Affiliation(s)
- Jakub Spiechowicz
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
- Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów, Poland
| | - Jerzy Łuczka
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
- Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów, Poland
| | - Peter Hänggi
- Institute of Physics, University of Augsburg, 86135 Augsburg, Germany
- Nanosystems Initiative Munich, Schellingstr, 4, D-80799 Műnchen, Germany
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22
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Mukhopadhyay AK, Liebchen B, Wulf T, Schmelcher P. Freezing, accelerating, and slowing directed currents in real time with superimposed driven lattices. Phys Rev E 2016; 93:052219. [PMID: 27300892 DOI: 10.1103/physreve.93.052219] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2016] [Indexed: 06/06/2023]
Abstract
We provide a generic scheme offering real-time control of directed particle transport using superimposed driven lattices. This scheme allows one to accelerate, slow, and freeze the transport on demand by switching one of the lattices subsequently on and off. The underlying physical mechanism hinges on a systematic opening and closing of channels between transporting and nontransporting phase space structures upon switching and exploits cantori structures which generate memory effects in the population of these structures. Our results should allow for real-time control of cold thermal atomic ensembles in optical lattices but might also be useful as a design principle for targeted delivery of molecules or colloids in optical devices.
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Affiliation(s)
- Aritra K Mukhopadhyay
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Benno Liebchen
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Thomas Wulf
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Peter Schmelcher
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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23
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Grossert C, Leder M, Denisov S, Hänggi P, Weitz M. Experimental control of transport resonances in a coherent quantum rocking ratchet. Nat Commun 2016; 7:10440. [PMID: 26852803 PMCID: PMC4748114 DOI: 10.1038/ncomms10440] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2015] [Accepted: 12/10/2015] [Indexed: 01/04/2023] Open
Abstract
The ratchet phenomenon is a means to get directed transport without net forces. Originally conceived to rectify stochastic motion and describe operational principles of biological motors, the ratchet effect can be used to achieve controllable coherent quantum transport. This transport is an ingredient of several perspective quantum devices including atomic chips. Here we examine coherent transport of ultra-cold atoms in a rocking quantum ratchet. This is realized by loading a rubidium atomic Bose–Einstein condensate into a periodic optical potential subjected to a biharmonic temporal drive. The achieved long-time coherence allows us to resolve resonance enhancement of the atom transport induced by avoided crossings in the Floquet spectrum of the system. By tuning the strength of the temporal modulations, we observe a bifurcation of a single resonance into a doublet. Our measurements reveal the role of interactions among Floquet eigenstates for quantum ratchet transport. The ratchet effect can be used as a tool to control coherent quantum transport of ultra-cold atoms. Here, the authors demonstrate a rocking quantum ratchet with a rubidium BEC, and reveal the existence of quantum transport resonances.
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Affiliation(s)
- Christopher Grossert
- Institut für Angewandte Physik der Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
| | - Martin Leder
- Institut für Angewandte Physik der Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
| | - Sergey Denisov
- Department of Applied Mathematics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603950, Russia.,Institut für Physik, Universität Augsburg, Universitätsstr. 1, 86159 Augsburg, Germany.,Sumy State University, Rimsky-Korsakov Street 2, 40007 Sumy, Ukraine
| | - Peter Hänggi
- Department of Applied Mathematics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603950, Russia.,Institut für Physik, Universität Augsburg, Universitätsstr. 1, 86159 Augsburg, Germany.,Nanosystems Initiative Munich, Schellingstr. 4, D-80799 München, Germany
| | - Martin Weitz
- Institut für Angewandte Physik der Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
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24
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Cubero D, Renzoni F. Hidden Symmetries, Instabilities, and Current Suppression in Brownian Ratchets. PHYSICAL REVIEW LETTERS 2016; 116:010602. [PMID: 26799008 DOI: 10.1103/physrevlett.116.010602] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2015] [Indexed: 06/05/2023]
Abstract
The operation of Brownian motors is usually described in terms of out-of-equilibrium and symmetry-breaking settings, with the relevant spatiotemporal symmetries identified from the analysis of the equations of motion for the system at hand. When the appropriate conditions are satisfied, symmetry-related trajectories with opposite current are thought to balance each other, yielding suppression of transport. The direction of the current can be precisely controlled around these symmetry points by finely tuning the driving parameters. Here we demonstrate, by studying a prototypical Brownian ratchet system, the existence of hidden symmetries, which escape identification by the standard symmetry analysis, and which require different theoretical tools for their revelation. Furthermore, we show that system instabilities may lead to spontaneous symmetry breaking with unexpected generation of directed transport.
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Affiliation(s)
- David Cubero
- Departamento de Física Aplicada I, EUP, Universidad de Sevilla, Calle Virgen de África 7, 41011 Sevilla, Spain
| | - Ferruccio Renzoni
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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25
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Dinis L, Quintero NR. Nonsinusoidal current and current reversals in a gating ratchet. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:032920. [PMID: 25871185 DOI: 10.1103/physreve.91.032920] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2014] [Indexed: 06/04/2023]
Abstract
In this work, the ratchet dynamics of Brownian particles driven by an external sinusoidal (harmonic) force is investigated. The gating ratchet effect is observed when another harmonic is used to modulate the spatially symmetric potential in which the particles move. For small amplitudes of the harmonics, it is shown that the current (average velocity) of particles exhibits a sinusoidal shape as a function of a precise combination of the phases of both harmonics. By increasing the amplitudes of the harmonics beyond the small-limit regime, departures from the sinusoidal behavior are observed and current reversals can also be induced. These current reversals persist even for the overdamped dynamics of the particles.
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Affiliation(s)
- Luis Dinis
- Departamento de Física Atómica, Molecular y Nuclear, Universidad Complutense de Madrid, 28040 Madrid, Spain
- GISC-Grupo Interdisciplinar de Sistemas Complejos, Madrid, Spain
| | - Niurka R Quintero
- Instituto de Matemáticas de la Universidad de Sevilla (IMUS)
- Departamento de Física Aplicada I, E.P.S., Universidad de Sevilla, Calle Virgen de África 7, 41011 Sevilla, Spain
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26
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27
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Goldwin J, Venkatesh BP, O'Dell DHJ. Backaction-driven transport of Bloch oscillating atoms in ring cavities. PHYSICAL REVIEW LETTERS 2014; 113:073003. [PMID: 25170704 DOI: 10.1103/physrevlett.113.073003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2014] [Indexed: 06/03/2023]
Abstract
We predict that an atomic Bose-Einstein condensate strongly coupled to an intracavity optical lattice can undergo resonant tunneling and directed transport when a constant and uniform bias force is applied. The bias force induces Bloch oscillations, causing amplitude and phase modulation of the lattice which resonantly modifies the site-to-site tunneling. For the right choice of parameters a net atomic current is generated. The transport velocity can be oriented oppositely to the bias force, with its amplitude and direction controlled by the detuning between the pump laser and the cavity. The transport can also be enhanced through imbalanced pumping of the two counterpropagating running wave cavity modes. Our results add to the cold atoms quantum simulation toolbox, with implications for quantum sensing and metrology.
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Affiliation(s)
- J Goldwin
- Midlands Ultracold Atom Research Centre, School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
| | - B Prasanna Venkatesh
- Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4M1, Canada and Asia Pacific Center for Theoretical Physics, San 31, Hyoja-dong, Nam-gu, Pohang, Gyeongbuk 790-784, Korea
| | - D H J O'Dell
- Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4M1, Canada
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28
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Casado-Pascual J, Cubero D, Renzoni F. Universal asymptotic behavior in nonlinear systems driven by a two-frequency forcing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062919. [PMID: 24483543 DOI: 10.1103/physreve.88.062919] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2013] [Indexed: 06/03/2023]
Abstract
We examine the time-dependent behavior of a nonlinear system driven by a two-frequency forcing. By using a nonperturbative approach, we are able to derive an asymptotic expression, valid in the long-time limit, for the time average of the output variable which describes the response of the system. We identify several universal features of the asymptotic response of the system, which are independent of the details of the model. In particular, we determine an asymptotic expression for the width of the resonance observed by keeping one frequency fixed and varying the other one. We show that this width is smaller than the usually assumed Fourier width by a factor determined by the two driving frequencies, and independent of the model system parameters. Additional general features can also be identified depending on the specific symmetry properties of the system. Our results find direct application in the study of sub-Fourier signal processing with nonlinear systems.
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Affiliation(s)
- Jesús Casado-Pascual
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, 41080 Sevilla, Spain
| | - David Cubero
- Departamento de Física Aplicada I, EUP, Universidad de Sevilla, Calle Virgen de África 7, 41011 Sevilla, Spain
| | - Ferruccio Renzoni
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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29
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Berardi V, Lydon J, Kevrekidis PG, Daraio C, Carretero-González R. Directed ratchet transport in granular chains. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052202. [PMID: 24329254 DOI: 10.1103/physreve.88.052202] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2013] [Indexed: 06/03/2023]
Abstract
Directed-ratchet transport (DRT) in a one-dimensional lattice of spherical beads, which serves as a prototype for granular chains, is investigated. We consider a system where the trajectory of the central bead is prescribed by a biharmonic forcing function with broken time-reversal symmetry. By comparing the mean integrated force of beads equidistant from the forcing bead, two distinct types of directed transport can be observed-spatial and temporal DRT. Based on the value of the frequency of the forcing function relative to the cutoff frequency, the system can be categorized by the presence and magnitude of each type of DRT. Furthermore, we investigate and quantify how varying additional parameters such as the biharmonic weight affects DRT velocity and magnitude. Finally, friction is introduced into the system and is found to significantly inhibit spatial DRT. In fact, for sufficiently low forcing frequencies, the friction may even induce a switching of the DRT direction.
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Affiliation(s)
- V Berardi
- Nonlinear Dynamical Systems Group, Computational Science Research Center, and Department of Mathematics and Statistics, San Diego State University, San Diego, California 92182-7720, USA
| | - J Lydon
- Graduate Aeronautical Laboratories (GALCIT) and Department of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA and Department of Mechanical and Process Engineering, Swiss Federal Institute of Technology (ETH), Zürich, Switzerland
| | - P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
| | - C Daraio
- Graduate Aeronautical Laboratories (GALCIT) and Department of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA and Department of Mechanical and Process Engineering, Swiss Federal Institute of Technology (ETH), Zürich, Switzerland
| | - R Carretero-González
- Nonlinear Dynamical Systems Group, Computational Science Research Center, and Department of Mathematics and Statistics, San Diego State University, San Diego, California 92182-7720, USA
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30
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Windpassinger P, Sengstock K. Engineering novel optical lattices. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2013; 76:086401. [PMID: 23828639 DOI: 10.1088/0034-4885/76/8/086401] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Optical lattices have developed into a widely used and highly recognized tool to study many-body quantum physics with special relevance for solid state type systems. One of the most prominent reasons for this success is the high degree of tunability in the experimental setups. While at the beginning quasi-static, cubic geometries were mainly explored, the focus of the field has now shifted toward new lattice topologies and the dynamical control of lattice structures. In this review we intend to give an overview of the progress recently achieved in this field on the experimental side. In addition, we discuss theoretical proposals exploiting specifically these novel lattice geometries.
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Affiliation(s)
- Patrick Windpassinger
- Institut für Laserphysik and Zentrum für Optische Quantentechnologien, Universität Hamburg, Hamburg, Germany.
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31
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Arzola AV, Volke-Sepúlveda K, Mateos JL. Dynamical analysis of an optical rocking ratchet: theory and experiment. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:062910. [PMID: 23848751 DOI: 10.1103/physreve.87.062910] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2013] [Indexed: 06/02/2023]
Abstract
A thorough analysis of the dynamics in a deterministic optical rocking ratchet [introduced in A. V. Arzola et al., Phys. Rev. Lett. 106, 168104 (2011)] and a comparison with experimental results are presented. The studied system consists of a microscopic particle interacting with a periodic and asymmetric light pattern, which is driven away from equilibrium by means of an unbiased time-periodic external force. It is shown that the asymmetry of the effective optical potential depends on the relative size of the particle with respect to the spatial period, and this is analyzed as an effective mechanism for particle fractionation. The necessary conditions to obtain current reversals in the deterministic regime are discussed in detail.
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Affiliation(s)
- Alejandro V Arzola
- Institute of Scientific Instruments of the ASCR, v.v.i., Academy of Sciences of the Czech Republic, Královopolská 147, 612 64 Brno, Czech Republic.
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32
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Kato A, Tanimura Y. Quantum Suppression of Ratchet Rectification in a Brownian System Driven by a Biharmonic Force. J Phys Chem B 2013; 117:13132-44. [DOI: 10.1021/jp403056h] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Akihito Kato
- Department
of Chemistry, Graduate
School of Science, Kyoto University, Kyoto606-8502,
Japan
| | - Yoshitaka Tanimura
- Department
of Chemistry, Graduate
School of Science, Kyoto University, Kyoto606-8502,
Japan
- Universität Augsburg, Institut für Physik, Universitätsstrasse
1, 86135 Augsburg, Germany
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33
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Itin AP, Neishtadt AI. Directed transport in a classical lattice with a high-frequency driving. Phys Rev E 2012; 86:016206. [PMID: 23005506 DOI: 10.1103/physreve.86.016206] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2012] [Revised: 04/10/2012] [Indexed: 11/07/2022]
Abstract
We analyze the dynamics of a classical particle in a spatially periodic potential under the influence of a periodic in time uniform force. It was shown by S. Flach and coworkers [Phys. Rev. Lett. 84, 2358 (2000)] that despite zero average force, directed transport is possible in the system. Asymptotic description of this phenomenon for the case of slow driving was developed by X. Leoncini and coworkers [Phys. Rev. E 79, 026213 (2009)]. Here we consider the case of fast driving using the canonical perturbation theory. An asymptotic formula is derived for the average drift velocity as a function of the system parameters and the driving law. We show that directed transport arises in an effective Hamiltonian that does not possess chaotic dynamics, thereby clarifying the relation between chaos and transport in the system. Sufficient conditions for transport are derived.
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Affiliation(s)
- A P Itin
- Zentrum für optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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34
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Watanabe G, Yoon S, Dalfovo F. Swallowtail band structure of the superfluid Fermi gas in an optical lattice. PHYSICAL REVIEW LETTERS 2011; 107:270404. [PMID: 22243294 DOI: 10.1103/physrevlett.107.270404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2011] [Indexed: 05/31/2023]
Abstract
We investigate the energy band structure of the superfluid flow of ultracold dilute Fermi gases in a one-dimensional optical lattice along the BCS to Bose-Einstein condensate (BEC) crossover within a mean-field approach. In each side of the crossover region, a loop structure (swallowtail) appears in the Bloch energy band of the superfluid above a critical value of the interaction strength. The width of the swallowtail is largest near unitarity. Across the critical value of the interaction strength, the profiles of density and pairing field change more drastically in the BCS side than in the BEC side. It is found that along with the appearance of the swallowtail, there exists a narrow band in the quasiparticle energy spectrum close to the chemical potential, and the incompressibility of the Fermi gas consequently experiences a profound dip in the BCS side, unlike in the BEC side.
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Affiliation(s)
- Gentaro Watanabe
- Asia Pacific Center for Theoretical Physics (APCTP), Pohang, Gyeongbuk, Korea
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35
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Yu HF, Zhu XB, Peng ZH, Tian Y, Cui DJ, Chen GH, Zheng DN, Jing XN, Lu L, Zhao SP, Han S. Quantum phase diffusion in a small underdamped Josephson junction. PHYSICAL REVIEW LETTERS 2011; 107:067004. [PMID: 21902362 DOI: 10.1103/physrevlett.107.067004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2010] [Indexed: 05/27/2023]
Abstract
Quantum phase diffusion in a small underdamped Nb/AlO(x)/Nb junction (∼0.4 μm(2)) is demonstrated in a wide temperature range of 25-140 mK where macroscopic quantum tunneling (MQT) is the dominant escape mechanism. We propose a two-step transition model to describe the switching process in which the escape rate out of the potential well and the transition rate from phase diffusion to the running state are considered. The transition rate extracted from the experimental switching current distribution follows the predicted Arrhenius law in the thermal regime but is greatly enhanced when MQT becomes dominant.
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Affiliation(s)
- H F Yu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, China
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36
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Hennig D, Burbanks AD, Osbaldestin AH. Directed current in the Holstein system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:031121. [PMID: 21517468 DOI: 10.1103/physreve.83.031121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2010] [Revised: 12/15/2010] [Indexed: 05/30/2023]
Abstract
We propose a mechanism to rectify charge transport in the semiclassical Holstein model. It is shown that localized initial conditions associated with a polaron solution, in conjunction with static electron on-site potential not having inversion symmetry, constitute minimal prerequisites for the emergence of a directed current in the underlying periodic lattice system. In particular, we demonstrate that for unbiased spatially localized initial conditions (constituted by kicked static polaron states), violation of parity prevents the existence of pairs of counterpropagating trajectories, thus allowing for a directed current despite the time reversibility of the equations of motion. Nevertheless, propagating polaron solutions associated with sets of unbiased localized initial conditions which eventually leave the region of localized initial conditions do not exhibit time reversibility. Since the initial conditions belonging to the corresponding counterpropagating, current-compensating polaron solutions are not contained in the set, this gives rise to the emergence of a current. Occurrence of long-range coherent charge transport is demonstrated.
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Affiliation(s)
- D Hennig
- Department of Mathematics, University of Portsmouth, Portsmouth PO13HF, United Kingdom
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37
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Polson JM, Bylhouwer B, Zuckermann MJ, Horton AJ, Scott WM. Dynamics of a polymer in a Brownian ratchet. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:051931. [PMID: 21230524 DOI: 10.1103/physreve.82.051931] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2010] [Revised: 09/29/2010] [Indexed: 05/30/2023]
Abstract
We have used Brownian dynamics simulations to study the dynamics of a bead-and-spring polymer subject to a flashing ratchet potential. To elucidate the role of hydrodynamic (HD) interactions, simulations were carried out for the cases where HD interactions are present and when they are absent. The average speed of the polymer and its conformational properties were examined upon variation in the polymer length, N, and the ratchet spatial period, L. Two distinct dynamical regimes were evident. In the low-N/high-L regime, the velocity decreases with increasing N, and center-of-mass diffusion is a key part of the motional mechanism. By contrast, in the high-N /low-L regime, the velocity is insensitive to variation in N, and motion is achieved via the coupling of internal modes to the cycling of the ratchet potential. The location of the regimes is correlated with the average conformational state of the polymer. Incorporating HD interactions increases the average polymer velocity for all polymer lengths and ratchet spatial periods considered. The dynamical behavior of polymers in the low-N/high-L regime can be understood using simple a theoretical model that yields quantitatively reasonable predictions of the polymer velocity.
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Affiliation(s)
- James M Polson
- Department of Physics, University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada C1A 4P3
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38
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Machura L, Łuczka J. Transport driven by biharmonic forces: impact of correlated thermal noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:031133. [PMID: 21230051 DOI: 10.1103/physreve.82.031133] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2010] [Indexed: 05/30/2023]
Abstract
We study an inertial brownian particle moving in a symmetric periodic substrate, driven by a zero-mean biharmonic force and correlated thermal noise. The brownian motion is described in terms of a generalized Langevin equation with an exponentially correlated gaussian noise term, obeying the fluctuation-dissipation theorem. We analyze impact of nonzero correlation time of thermal noise on transport properties of the brownian particle. We identify regimes where the increase of the correlation time intensifies long-time transport of the brownian particle. The opposite effect is also found: longer correlation time reduces the stationary velocity of the particle. The correlation time induced multiple current reversal is detected. We reveal that thermal noise of nonzero correlation time can radically enhance long-time velocity of the brownian particle in regimes where in the white noise limit the velocity is extremely small. All transport properties can be tested in the setup consisting of a resistively and capacitively shunted Josephson junction device.
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Affiliation(s)
- L Machura
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
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40
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Hennig D, Burbanks AD, Mulhern C, Osbaldestin AH. Emergence of continual directed flow in hamiltonian systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:026210. [PMID: 20866896 DOI: 10.1103/physreve.82.026210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2010] [Revised: 05/07/2010] [Indexed: 05/29/2023]
Abstract
We propose a minimal model for the emergence of a directed flow in autonomous hamiltonian systems. It is shown that internal breaking of the spatiotemporal symmetries, via localized initial conditions, which are unbiased with respect to the transporting degree of freedom, and transient chaos conspire to form the physical mechanism for the occurrence of a current. Most importantly, after passage through the transient chaos, trajectories perform solely regular transporting motion so that the resulting current is of continual ballistic nature. This has to be distinguished from the features of transport reported previously for driven hamiltonian systems with mixed phase space where transport is determined by intermittent behavior exhibiting power-law decay statistics of the duration of regular ballistic periods.
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Affiliation(s)
- D Hennig
- Department of Mathematics, University of Portsmouth, Portsmouth PO1 3HF, UK
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41
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Petri C, Lenz F, Diakonos FK, Schmelcher P. Directed transport and localization in phase-modulated driven lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:046219. [PMID: 20481819 DOI: 10.1103/physreve.81.046219] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2010] [Indexed: 05/29/2023]
Abstract
We explore the dynamics of noninteracting particles loaded into a phase-modulated one-dimensional lattice formed by laterally oscillating square barriers. Tuning the parameters of the driven unit cell of the lattice selected parts of the classical phase space can be manipulated in a controllable manner. We find superdiffusion in position space for all parameters regimes. A directed current of an ensemble of particles can be created through locally breaking the spatiotemporal symmetries of the time-driven potential. Magnitude and direction of the current are tunable. Several mechanisms for transient localization and trapping of particles in different wells of the driven unit cell are presented and analyzed.
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Affiliation(s)
- Christoph Petri
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany.
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42
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Quintero NR, Cuesta JA, Alvarez-Nodarse R. Symmetries shape the current in ratchets induced by a biharmonic driving force. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:030102. [PMID: 20365682 DOI: 10.1103/physreve.81.030102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2009] [Revised: 12/15/2009] [Indexed: 05/29/2023]
Abstract
Equations describing the evolution of particles, solitons, or localized structures, driven by a zero-average, periodic, external force, and invariant under time reversal and a half-period time shift, exhibit a ratchet current when the driving force breaks these symmetries. The biharmonic force f(t)=1 cos(qomegat+phi1)+2 cospomegat+phi2) does it for almost any choice of vphi1 and phi2, provided p and q are two coprime integers such that p+q is odd. It has been widely observed, in experiments in semiconductors, in Josephson junctions, photonic crystals, etc., as well as in simulations, that the ratchet current induced by this force has the shape v proportional, variant1p2q cos(pphi1-qphi2+theta0) for small amplitudes, where theta0 depends on the damping ( theta0=pi/2 if there is no damping, and theta0=0 for overdamped systems). We rigorously prove that this precise shape can be obtained solely from the broken symmetries of the system and is independent of the details of the equation describing the system.
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Affiliation(s)
- Niurka R Quintero
- Departamento de Física Aplicada I, EUP, Universidad de Sevilla, Virgen de Africa 7, E-41011 Sevilla, Spain.
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Salger T, Kling S, Hecking T, Geckeler C, Morales-Molina L, Weitz M. Directed transport of atoms in a Hamiltonian quantum ratchet. Science 2009; 326:1241-3. [PMID: 19965469 DOI: 10.1126/science.1179546] [Citation(s) in RCA: 179] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Classical ratchet potentials, which alternate a driving potential with periodic random dissipative motion, can account for the operation of biological motors. We demonstrate the operation of a quantum ratchet, which differs from classical ratchets in that dissipative processes are absent within the observation time of the system (Hamiltonian regime). An atomic rubidium Bose-Einstein condensate is exposed to a sawtooth-like optical lattice potential, whose amplitude is periodically modulated in time. The ratchet transport arises from broken spatiotemporal symmetries of the driven potential, resulting in a desymmetrization of transporting eigenstates (Floquet states). The full quantum character of the ratchet transport was demonstrated by the measured atomic current oscillating around a nonzero stationary value at longer observation times, resonances occurring at positions determined by the photon recoil, and dependence of the transport current on the initial phase of the driving potential.
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Affiliation(s)
- Tobias Salger
- Institut für Angewandte Physik, Wegelerstrasse 8, 53115 Bonn, Germany.
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Reimann P, Eichhorn R. Weak disorder strongly improves the selective enhancement of diffusion in a tilted periodic potential. PHYSICAL REVIEW LETTERS 2008; 101:180601. [PMID: 18999809 DOI: 10.1103/physrevlett.101.180601] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2008] [Indexed: 05/27/2023]
Abstract
The diffusion of an overdamped Brownian particle in a tilted periodic potential is known to exhibit a pronounced enhancement over the free thermal diffusion within a small interval of tilt values. Here we show that weak disorder in the form of small, time-independent deviations from a strictly spatially periodic potential may further boost this diffusion peak by orders of magnitude. Our general theoretical predictions are in excellent agreement with experimental observations.
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Affiliation(s)
- Peter Reimann
- Universität Bielefeld, Fakultät für Physik, 33615 Bielefeld, Germany
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45
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Franco I, Shapiro M, Brumer P. Femtosecond dynamics and laser control of charge transport in trans-polyacetylene. J Chem Phys 2008; 128:244905. [PMID: 18601381 DOI: 10.1063/1.2940789] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The induction of dc electronic transport in rigid and flexible trans-polyacetylene oligomers according to the omega versus 2omega coherent control scenario is investigated using a quantum-classical mean field approximation. The approach involves running a large ensemble of mixed quantum-classical trajectories under the influence of omega+2omega laser fields and choosing the initial conditions by sampling the ground-state Wigner distribution function for the nuclei. The vibronic couplings are shown to change the mean single-particle spectrum, introduce ultrafast decoherence, and enhance intramolecular vibrational and electronic relaxation. Nevertheless, even in the presence of significant couplings, limited coherent control of the electronic dynamics is still viable, the most promising route involving the use of femtosecond pulses with a duration that is comparable to the electronic dephasing time. The simulations offer a realistic description of the behavior of a simple coherent control scenario in a complex system and provide a detailed account of the femtosecond photoinduced vibronic dynamics of a conjugated polymer.
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Affiliation(s)
- Ignacio Franco
- Chemical Physics Theory Group, Department of Chemistry and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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46
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Denisov S, Zolotaryuk Y, Flach S, Yevtushenko O. Vortex and translational currents due to broken time-space symmetries. PHYSICAL REVIEW LETTERS 2008; 100:224102. [PMID: 18643422 DOI: 10.1103/physrevlett.100.224102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2008] [Indexed: 05/26/2023]
Abstract
We consider the classical dynamics of a particle in a (d=2,3)-dimensional space-periodic potential under the influence of time-periodic external fields with zero mean. We perform a general time-space symmetry analysis and identify conditions, when the particle will generate a nonzero averaged translational and vortex currents. We perform computational studies of the equations of motion and of corresponding Fokker-Planck equations, which confirm the symmetry predictions. We address the experimentally important issue of current control. Cold atoms in optical potentials and magnetic traps are among possible candidates to observe these findings experimentally.
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Affiliation(s)
- S Denisov
- Institut für Physik, Universität Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany
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47
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Gommers R, Lebedev V, Brown M, Renzoni F. Gating ratchet for cold atoms. PHYSICAL REVIEW LETTERS 2008; 100:040603. [PMID: 18352250 DOI: 10.1103/physrevlett.100.040603] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2007] [Revised: 10/30/2007] [Indexed: 05/26/2023]
Abstract
We demonstrate experimentally a gating ratchet with cold rubidium atoms in a driven near-resonant optical lattice. A single-harmonic periodic modulation of the optical potential depth is applied, together with a single-harmonic rocking force. Directed motion is observed as a result of the breaking of the symmetries of the system.
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Affiliation(s)
- R Gommers
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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48
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Dana I, Ramareddy V, Talukdar I, Summy GS. Experimental realization of quantum-resonance ratchets at arbitrary quasimomenta. PHYSICAL REVIEW LETTERS 2008; 100:024103. [PMID: 18232872 DOI: 10.1103/physrevlett.100.024103] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2007] [Revised: 08/30/2007] [Indexed: 05/25/2023]
Abstract
Quantum-resonance ratchets associated with the kicked particle are experimentally realized for arbitrary quasimomentum using a Bose-Einstein condensate (BEC) exposed to a pulsed standing light wave. The ratchet effect for general quasimomentum arises even though both the standing-wave potential and the initial state of the BEC have a point symmetry. The experimental results agree well with theoretical ones which take into account the finite quasimomentum width of the BEC. In particular, this width is shown to cause a suppression of the ratchet acceleration for exactly resonant quasimomentum, leading to a saturation of the directed current.
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Affiliation(s)
- I Dana
- Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
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49
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Ermann L, Carlo GG, Saraceno M. Transport phenomena in the asymmetric quantum multibaker map. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:011126. [PMID: 18351837 DOI: 10.1103/physreve.77.011126] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2007] [Indexed: 05/26/2023]
Abstract
By studying a modified (unbiased) quantum multibaker map, we were able to obtain a finite asymptotic quantum current without a classical analog. This result suggests a general method for the design of purely quantum ratchets and sheds light on the investigation of the mechanisms leading to net transport generation by breaking symmetries of quantum systems. Moreover, we propose the multibaker map as a resource to study directed transport phenomena in chaotic systems without bias. In fact, this is a paradigmatic model in classical and quantum chaos, but also in statistical mechanics.
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Affiliation(s)
- Leonardo Ermann
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
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50
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Zamora-Sillero E, Quintero NR, Mertens FG. Sine-Gordon ratchets with general periodic, additive, and parametric driving forces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:066601. [PMID: 18233931 DOI: 10.1103/physreve.76.066601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2007] [Indexed: 05/25/2023]
Abstract
We study the soliton ratchets in the damped sine-Gordon equation with periodic nonsinusoidal, additive, and parametric driving forces. By means of symmetry analysis of this system we show that the net motion of the kink is not possible if the frequencies of both forces satisfy a certain relationship. Using a collective coordinate theory with two degrees of freedom, we show that the ratchet motion of kinks appears as a consequence of a resonance between the oscillations of the momentum and the width of the kink. We show that the equations of motion that fulfill these collective coordinates follow from the corresponding symmetry properties of the original systems. As a further application of the collective coordinate technique we obtain another relationship between the frequencies of the parametric and additive drivers that suppresses the ratchetlike motion of the kink. We check all these results by means of numerical simulations of the original system and the numerical solutions of the collective coordinate equations.
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Affiliation(s)
- Elías Zamora-Sillero
- Departamento de Física Aplicada I, E. U. P., Universidad de Sevilla, Virgen de Africa 7, 41011 Sevilla, Spain.
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