1
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Wang F, Greenaway MT, Balanov AG, Fromhold TM. Non-KAM classical chaos topology for electrons in superlattice minibands determines the inter-well quantum transition rates. Sci Rep 2024; 14:5269. [PMID: 38438388 PMCID: PMC10912705 DOI: 10.1038/s41598-024-52351-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2023] [Accepted: 01/17/2024] [Indexed: 03/06/2024] Open
Abstract
We investigate the quantum-classical correspondence for a particle tunnelling through a periodic superlattice structure with an applied bias voltage and an additional tilted harmonic oscillator potential. We show that the quantum mechanical tunnelling rate between neighbouring quantum wells of the superlattice is determined by the topology of the phase trajectories of the analogous classical system. This result also enables us to estimate, with high accuracy, the tunnelling rate between two spatially displaced simple harmonic oscillator states using a classical model, and thus gain new insight into this generic quantum phenomenon. This finding opens new directions for exploring and understanding the quantum-classical correspondence principle and quantum jumps between displaced harmonic oscillators, which are important in many branches of natural science.
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Affiliation(s)
- F Wang
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, UK
| | - M T Greenaway
- Department of Physics, Loughborough University, Loughborough, LE11 3TU, UK
| | - A G Balanov
- Department of Physics, Loughborough University, Loughborough, LE11 3TU, UK
| | - T M Fromhold
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, UK.
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2
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Varikuti ND, Sahu A, Lakshminarayan A, Madhok V. Probing dynamical sensitivity of a non-Kolmogorov-Arnold-Moser system through out-of-time-order correlators. Phys Rev E 2024; 109:014209. [PMID: 38366507 DOI: 10.1103/physreve.109.014209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 12/06/2023] [Indexed: 02/18/2024]
Abstract
Non-Kolmogorov-Arnold-Moser (KAM) systems, when perturbed by weak time-dependent fields, offer a fast route to classical chaos through an abrupt breaking of invariant phase-space tori. In this work, we employ out-of-time-order correlators (OTOCs) to study the dynamical sensitivity of a perturbed non-KAM system in the quantum limit as the parameter that characterizes the resonance condition is slowly varied. For this purpose, we consider a quantized kicked harmonic oscillator (KHO) model, which displays stochastic webs resembling Arnold's diffusion that facilitate large-scale diffusion in the phase space. Although the Lyapunov exponent of the KHO at resonances remains close to zero in the weak perturbative regime, making the system weakly chaotic in the conventional sense, the classical phase space undergoes significant structural changes. Motivated by this, we study the OTOCs when the system is in resonance and contrast the results with the nonresonant case. At resonances, we observe that the long-time dynamics of the OTOCs are sensitive to these structural changes, where they grow quadratically as opposed to linear or stagnant growth at nonresonances. On the other hand, our findings suggest that the short-time dynamics remain relatively more stable and show the exponential growth found in the literature for unstable fixed points. The numerical results are backed by analytical expressions derived for a few special cases. We will then extend our findings concerning the nonresonant cases to a broad class of near-integrable KAM systems.
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Affiliation(s)
- Naga Dileep Varikuti
- Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India and Center for Quantum Information, Communication and Computation, Indian Institute of Technology Madras, Chennai 600036, India
| | - Abinash Sahu
- Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India and Center for Quantum Information, Communication and Computation, Indian Institute of Technology Madras, Chennai 600036, India
| | - Arul Lakshminarayan
- Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India and Center for Quantum Information, Communication and Computation, Indian Institute of Technology Madras, Chennai 600036, India
| | - Vaibhav Madhok
- Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India and Center for Quantum Information, Communication and Computation, Indian Institute of Technology Madras, Chennai 600036, India
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3
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Terragni F, Bonilla LL, Vega JM. Uncovering spatiotemporal patterns in semiconductor superlattices by efficient data processing tools. Phys Rev E 2021; 104:035303. [PMID: 34654121 DOI: 10.1103/physreve.104.035303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Accepted: 08/17/2021] [Indexed: 06/13/2023]
Abstract
Time periodic patterns in a semiconductor superlattice, relevant to microwave generation, are obtained upon numerical integration of a known set of drift-diffusion equations. The associated spatiotemporal transport mechanisms are uncovered by applying (to the computed data) two recent data processing tools, known as the higher order dynamic mode decomposition and the spatiotemporal Koopman decomposition. Outcomes include a clear identification of the asymptotic self-sustained oscillations of the current density (isolated from the transient dynamics) and an accurate description of the electric field traveling pulse in terms of its dispersion diagram. In addition, a preliminary version of a data-driven reduced order model is constructed, which allows for extremely fast online simulations of the system response over a range of different configurations.
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Affiliation(s)
- F Terragni
- G. Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, and Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - L L Bonilla
- G. Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, and Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - J M Vega
- E.T.S.I. Aeronáutica y del Espacio, Universidad Politécnica de Madrid, 28040 Madrid, Spain
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4
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Quasiadiabatic electron transport in room temperature nanoelectronic devices induced by hot-phonon bottleneck. Nat Commun 2021; 12:4752. [PMID: 34362908 PMCID: PMC8346506 DOI: 10.1038/s41467-021-25094-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2020] [Accepted: 07/18/2021] [Indexed: 12/02/2022] Open
Abstract
Since the invention of transistors, the flow of electrons has become controllable in solid-state electronics. The flow of energy, however, remains elusive, and energy is readily dissipated to lattice via electron-phonon interactions. Hence, minimizing the energy dissipation has long been sought by eliminating phonon-emission process. Here, we report a different scenario for facilitating energy transmission at room temperature that electrons exert diffusive but quasiadiabatic transport, free from substantial energy loss. Direct nanothermometric mapping of electrons and lattice in current-carrying GaAs/AlGaAs devices exhibit remarkable discrepancies, indicating unexpected thermal isolation between the two subsystems. This surprising effect arises from the overpopulated hot longitudinal-optical (LO) phonons generated through frequent emission by hot electrons, which induce equally frequent LO-phonon reabsorption (“hot-phonon bottleneck”) cancelling the net energy loss. Our work sheds light on energy manipulation in nanoelectronics and power-electronics and provides important hints to energy-harvesting in optoelectronics (such as hot-carrier solar-cells). Minimizing the energy dissipation is usually sought by eliminating phonon-emission process. Here, the authors find a different approach for facilitating energy transmission at room temperature that electrons exert diffusive but quasiadiabatic transport, free from substantial energy loss.
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5
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Li K, Zhang C, Wu Y, Lin W, Zheng X, Zhou Y, Lu S, Kang J. In-plane Anisotropy of Quantum Transport in Artificial Two-dimensional Au Lattices. NANO LETTERS 2018; 18:1724-1732. [PMID: 29433320 DOI: 10.1021/acs.nanolett.7b04783] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We report an experimental observation and direct control of quantum transport in artificial two-dimensional Au lattices. Combining the advanced techniques of low-temperature deposition and newly developed double-probe scanning tunneling spectroscopy, we display a two-dimensional carrier transport and demonstrate a strong in-plane transport modulation in the two-dimensional Au lattices. In well-ordered Au lattices, we observe the carrier transport behavior manifesting as a band-like feature with an energy gap. Furthermore, controlled structural modification performed by constructing coupled "stadiums" enables a transition of system dynamics in the lattices, which in turn establishes tunable resonant transport throughout a wide energy range. Our findings open the possibility of the construction and transport engineering of artificial lattices by the geometrical arrangement of scatterers and quantum chaotic dynamics.
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Affiliation(s)
- Kongyi Li
- Department of Physics, OSED, Fujian Provincial Key Laboratory of Semiconductors Materials and Applications , Xiamen University , Xiamen 361005 , China
- Department of Applied Physics , Eindhoven University of Technology , P.O. Box 513, 5600 MB Eindhoven , The Netherlands
| | - Chunmiao Zhang
- Department of Physics, OSED, Fujian Provincial Key Laboratory of Semiconductors Materials and Applications , Xiamen University , Xiamen 361005 , China
| | - Yaping Wu
- Department of Physics, OSED, Fujian Provincial Key Laboratory of Semiconductors Materials and Applications , Xiamen University , Xiamen 361005 , China
| | - Wenzhi Lin
- Department of Physics, OSED, Fujian Provincial Key Laboratory of Semiconductors Materials and Applications , Xiamen University , Xiamen 361005 , China
| | - Xuanli Zheng
- Department of Physics, OSED, Fujian Provincial Key Laboratory of Semiconductors Materials and Applications , Xiamen University , Xiamen 361005 , China
| | - Yinghui Zhou
- Department of Physics, OSED, Fujian Provincial Key Laboratory of Semiconductors Materials and Applications , Xiamen University , Xiamen 361005 , China
| | - Shiqiang Lu
- Department of Physics, OSED, Fujian Provincial Key Laboratory of Semiconductors Materials and Applications , Xiamen University , Xiamen 361005 , China
| | - Junyong Kang
- Department of Physics, OSED, Fujian Provincial Key Laboratory of Semiconductors Materials and Applications , Xiamen University , Xiamen 361005 , China
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6
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Bonilla LL, Carretero M, Segura A. Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice. Phys Rev E 2018; 96:062215. [PMID: 29347331 DOI: 10.1103/physreve.96.062215] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2017] [Indexed: 11/07/2022]
Abstract
When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.
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Affiliation(s)
- L L Bonilla
- Gregorio Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, and Department of Materials Science and Engineering and Chemical Engineering, Universidad Carlos III de Madrid, Leganés, Spain
| | - M Carretero
- Gregorio Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, and Department of Materials Science and Engineering and Chemical Engineering, Universidad Carlos III de Madrid, Leganés, Spain
| | - A Segura
- Gregorio Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, and Department of Materials Science and Engineering and Chemical Engineering, Universidad Carlos III de Madrid, Leganés, Spain
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7
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Ying L, Huang D, Lai YC. Multistability, chaos, and random signal generation in semiconductor superlattices. Phys Rev E 2016; 93:062204. [PMID: 27415252 DOI: 10.1103/physreve.93.062204] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2016] [Indexed: 06/06/2023]
Abstract
Historically, semiconductor superlattices, artificial periodic structures of different semiconductor materials, were invented with the purpose of engineering or manipulating the electronic properties of semiconductor devices. A key application lies in generating radiation sources, amplifiers, and detectors in the "unusual" spectral range of subterahertz and terahertz (0.1-10 THz), which cannot be readily realized using conventional radiation sources, the so-called THz gap. Efforts in the past three decades have demonstrated various nonlinear dynamical behaviors including chaos, suggesting the potential to exploit chaos in semiconductor superlattices as random signal sources (e.g., random number generators) in the THz frequency range. We consider a realistic model of hot electrons in semiconductor superlattice, taking into account the induced space charge field. Through a systematic exploration of the phase space we find that, when the system is subject to an external electrical driving of a single frequency, chaos is typically associated with the occurrence of multistability. That is, for a given parameter setting, while there are initial conditions that lead to chaotic trajectories, simultaneously there are other initial conditions that lead to regular motions. Transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt. Multistability thus presents an obstacle to utilizing the superlattice system as a reliable and robust random signal source. However, we demonstrate that, when an additional driving field of incommensurate frequency is applied, multistability can be eliminated, with chaos representing the only possible asymptotic behavior of the system. In such a case, a random initial condition will lead to a trajectory landing in a chaotic attractor with probability 1, making quasiperiodically driven semiconductor superlattices potentially as a reliable device for random signal generation to fill the THz gap. The interplay among noise, multistability, and chaos is also investigated.
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Affiliation(s)
- Lei Ying
- School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
| | - Danhong Huang
- Air Force Research Laboratory, Space Vehicles Directorate, Kirtland Air Force Base, New Mexico 87117, USA
- Center for High Technology Materials, University of New Mexico, 1313 Goddard St. SE, Albuquerque, New Mexico 87106, USA
| | - Ying-Cheng Lai
- School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
- Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
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8
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Paul S, Pal H, Santhanam MS. Barrier-induced chaos in a kicked rotor: Classical subdiffusion and quantum localization. Phys Rev E 2016; 93:060203. [PMID: 27415192 DOI: 10.1103/physreve.93.060203] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2016] [Indexed: 06/06/2023]
Abstract
The relation between classically chaotic dynamics and quantum localization is studied in a system that violates the assumptions of the Kolmogorov-Arnold-Moser (KAM) theorem, namely, the kicked rotor in a discontinuous potential barrier. We show that the discontinuous barrier induces chaos and more than two distinct subdiffusive energy growth regimes, the latter being an unusual feature for Hamiltonian chaos. We show that the dynamical localization in the quantized version of this system carries the imprint of non-KAM classical dynamics through the dependence of quantum break time on subdiffusion exponents. We briefly comment on the experimental feasibility of this system.
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Affiliation(s)
- Sanku Paul
- Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
| | - Harinder Pal
- Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Codigo Postal 62210, Cuernavaca, Mexico
| | - M S Santhanam
- Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
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9
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Hramov AE, Makarov VV, Maximenko VA, Koronovskii AA, Balanov AG. Intermittency route to chaos and broadband high-frequency generation in semiconductor superlattice coupled to external resonator. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022911. [PMID: 26382480 DOI: 10.1103/physreve.92.022911] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2015] [Indexed: 06/05/2023]
Abstract
We investigate the onset of broadband microwave chaos in the miniband semiconductor superlattice coupled to an external resonator. Our analysis shows that the transition to chaos, which is confirmed by calculation of Lyapunov exponents, is associated with the intermittency scenario. The evolution of the laminar phases and the corresponding Poincare maps with variation of a supercriticality parameter suggest that the observed dynamics can be classified as type I intermittency. We study the spatiotemporal patterns of the charge concentration and discuss how the frequency band of the chaotic current oscillations in semiconductor superlattice depends on the voltage applied.
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Affiliation(s)
- Alexander E Hramov
- Research and Education Center 'Nonlinear Dynamics of Complex Systems', Saratov State Technical University, Saratov 410054, Russia
- Faculty of Nonlinear Processes, Saratov State University, Astrakhanskaja 83, Saratov 410012, Russia
| | - Vladimir V Makarov
- Research and Education Center 'Nonlinear Dynamics of Complex Systems', Saratov State Technical University, Saratov 410054, Russia
- Faculty of Nonlinear Processes, Saratov State University, Astrakhanskaja 83, Saratov 410012, Russia
| | - Vladimir A Maximenko
- Research and Education Center 'Nonlinear Dynamics of Complex Systems', Saratov State Technical University, Saratov 410054, Russia
- Faculty of Nonlinear Processes, Saratov State University, Astrakhanskaja 83, Saratov 410012, Russia
| | - Alexey A Koronovskii
- Research and Education Center 'Nonlinear Dynamics of Complex Systems', Saratov State Technical University, Saratov 410054, Russia
- Faculty of Nonlinear Processes, Saratov State University, Astrakhanskaja 83, Saratov 410012, Russia
| | - Alexander G Balanov
- Research and Education Center 'Nonlinear Dynamics of Complex Systems', Saratov State Technical University, Saratov 410054, Russia
- Department of Physics, Loughborough University, Loughborough LE11 3TU, United Kingdom
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10
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Soskin SM, Khovanov IA, McClintock PVE. Regular rather than chaotic origin of the resonant transport in superlattices. PHYSICAL REVIEW LETTERS 2015; 114:166802. [PMID: 25955068 DOI: 10.1103/physrevlett.114.166802] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2014] [Indexed: 06/04/2023]
Abstract
We address the enhancement of electron transport in semiconductor superlattices that occurs in combined electric and magnetic fields when cyclotron rotation becomes resonant with Bloch oscillations. We show that the phenomenon is regular in origin, contrary to the widespread belief that it arises through chaotic diffusion. The theory verified by simulations provides an accurate description of earlier numerical results and suggests new ways of controlling resonant transport.
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Affiliation(s)
- S M Soskin
- Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, 03028 Kiev, Ukraine
- Physics Department, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - I A Khovanov
- School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
- Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - P V E McClintock
- Physics Department, Lancaster University, Lancaster LA1 4YB, United Kingdom
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11
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Hramov AE, Makarov VV, Koronovskii AA, Kurkin SA, Gaifullin MB, Alexeeva NV, Alekseev KN, Greenaway MT, Fromhold TM, Patanè A, Kusmartsev FV, Maksimenko VA, Moskalenko OI, Balanov AG. Subterahertz chaos generation by coupling a superlattice to a linear resonator. PHYSICAL REVIEW LETTERS 2014; 112:116603. [PMID: 24702398 DOI: 10.1103/physrevlett.112.116603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2013] [Indexed: 06/03/2023]
Abstract
We investigate the effects of a linear resonator on the high-frequency dynamics of electrons in devices exhibiting negative differential conductance. We show that the resonator strongly affects both the dc and ac transport characteristics of the device, inducing quasiperiodic and high-frequency chaotic current oscillations. The theoretical findings are confirmed by experimental measurements of a GaAs/AlAs miniband semiconductor superlattice coupled to a linear microstrip resonator. Our results are applicable to other active solid state devices and provide a generic approach for developing modern chaos-based high-frequency technologies including broadband chaotic wireless communication and superfast random-number generation.
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Affiliation(s)
- A E Hramov
- Faculty of Nonlinear Processes, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia and Saratov State Technical University, Politechnicheskaja 77, Saratov 410054, Russia
| | - V V Makarov
- Faculty of Nonlinear Processes, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia
| | - A A Koronovskii
- Faculty of Nonlinear Processes, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia and Saratov State Technical University, Politechnicheskaja 77, Saratov 410054, Russia
| | - S A Kurkin
- Faculty of Nonlinear Processes, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia
| | - M B Gaifullin
- Department of Physics, Loughborough University, Loughborough LE11 3TU, United Kingdom
| | - N V Alexeeva
- Department of Physics, Loughborough University, Loughborough LE11 3TU, United Kingdom
| | - K N Alekseev
- Department of Physics, Loughborough University, Loughborough LE11 3TU, United Kingdom
| | - M T Greenaway
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - T M Fromhold
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - A Patanè
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | | | - V A Maksimenko
- Saratov State Technical University, Politechnicheskaja 77, Saratov 410054, Russia
| | - O I Moskalenko
- Saratov State Technical University, Politechnicheskaja 77, Saratov 410054, Russia
| | - A G Balanov
- Department of Physics, Loughborough University, Loughborough LE11 3TU, United Kingdom
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12
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Lemos GB, Gomes RM, Walborn SP, Souto Ribeiro PH, Toscano F. Experimental observation of quantum chaos in a beam of light. Nat Commun 2012; 3:1211. [DOI: 10.1038/ncomms2214] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2012] [Accepted: 10/19/2012] [Indexed: 11/09/2022] Open
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13
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Brunner R, Ferry DK, Akis R, Meisels R, Kuchar F, Burke AM, Bird JP. Open quantum dots: II. Probing the classical to quantum transition. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:343202. [PMID: 22871799 DOI: 10.1088/0953-8984/24/34/343202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Open quantum dots provide a natural system in which to study both classical and quantum features of transport. From the classical point of view these dots possess a mixed phase space which yields families of closed, regular orbits as well as an expansive sea of chaos. An important question concerns the manner in which these classical states evolve into the set of quantum states that populate the dot in the quantum limit. In the reverse direction, the manner in which the quantum states evolve to the classical world is governed strongly by Zurek's decoherence theory. This was discussed from the quantum perspective in an earlier review (Ferry et al 2011 Semicond. Sci. Technol. 26 043001). Here, we discuss the nature of the various classical states, how they are formed, how they progress to the quantum world, and the signatures that they create in magnetotransport and general conductance studies of these dots.
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Affiliation(s)
- R Brunner
- Institut für Physik, Montanuniversitaet Leoben, A-8700 Leoben, Austria
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14
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Alexeeva N, Greenaway MT, Balanov AG, Makarovsky O, Patanè A, Gaifullin MB, Kusmartsev F, Fromhold TM. Controlling high-frequency collective electron dynamics via single-particle complexity. PHYSICAL REVIEW LETTERS 2012; 109:024102. [PMID: 23030163 DOI: 10.1103/physrevlett.109.024102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2011] [Indexed: 06/01/2023]
Abstract
We demonstrate, through experiment and theory, enhanced high-frequency current oscillations due to magnetically-induced conduction resonances in superlattices. Strong increase in the ac power originates from complex single-electron dynamics, characterized by abrupt resonant transitions between unbound and localized trajectories, which trigger and shape propagating charge domains. Our data demonstrate that external fields can tune the collective behavior of quantum particles by imprinting configurable patterns in the single-particle classical phase space.
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Affiliation(s)
- N Alexeeva
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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15
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Henning AJ, Fromhold TM, Wilkinson PB. Using dynamical barriers to control the transmission of light through slowly varying photonic crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:046209. [PMID: 21599272 DOI: 10.1103/physreve.83.046209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2010] [Revised: 12/17/2010] [Indexed: 05/30/2023]
Abstract
We use semiclassical Hamiltonian optics to investigate the propagation of light rays through two-dimensional photonic crystals when slow spatial modulation of the lattice parameters induces mixed stable-chaotic ray dynamics. This modulation changes both the shape and frequency range of the allowed frequency bands, thereby bending the resulting semiclassical ray trajectories and confining them within particular regions of the crystal. The curved boundaries of these regions, combined with the bending of the orbits themselves, creates a hierarchy of stable and unstable chaotic trajectories in phase space. For certain lattice parameters and electromagnetic wave frequencies, islands of stable orbits act as a dynamical barrier, which separates the chaotic trajectories into two distinct regions of the crystal, thereby preventing the rays propagating through the structure. We show that changing the frequency of the electromagnetic wave strongly affects the distribution of stable and unstable orbits in both real and phase space. This switches the dynamical barriers on and off and thus modulates the transmission of rays through the crystal. We propose microwave analogs of the photonic crystals as a route to the experimental study of the transport effects that we predict.
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Affiliation(s)
- A J Henning
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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16
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Pal H, Santhanam MS. Dynamics of kicked particles in a double-barrier structure. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:056212. [PMID: 21230568 DOI: 10.1103/physreve.82.056212] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2010] [Indexed: 05/30/2023]
Abstract
We study the classical and quantum dynamics of periodically kicked particles placed initially within an open double-barrier structure. This system does not obey the Kolmogorov-Arnold-Moser (KAM) theorem and displays chaotic dynamics. The phase-space features induced by non-KAM nature of the system lead to dynamical features such as the nonequilibrium steady state, classically induced saturation of energy growth and momentum filtering. We also comment on the experimental feasibility of this system as well as its relevance in the context of current interest in classically induced localization and chaotic ratchets.
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Affiliation(s)
- Harinder Pal
- Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India.
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17
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Zhou W, Chen Z, Zhang B, Yu CH, Lu W, Shen SC. Magnetic field control of the quantum chaotic dynamics of hydrogen analogs in an anisotropic crystal field. PHYSICAL REVIEW LETTERS 2010; 105:024101. [PMID: 20867709 DOI: 10.1103/physrevlett.105.024101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2010] [Indexed: 05/29/2023]
Abstract
We report magnetic field control of the quantum chaotic dynamics of hydrogen analogues in an anisotropic solid state environment. The chaoticity of the system dynamics was quantified by means of energy level statistics. We analyzed the magnetic field dependence of the statistical distribution of the impurity energy levels and found a smooth transition between the Poisson limit and the Wigner limit, i.e., transition between regular Poisson and fully chaotic Wigner dynamics. The effect of the crystal field anisotropy on the quantum chaotic dynamics, which manifests itself in characteristic transitions between regularity and chaos for different field orientations, was demonstrated.
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Affiliation(s)
- Weihang Zhou
- Surface Physics Laboratory, Department of Physics, and Laboratory of Advanced Materials, Fudan University, Shanghai 200433, People's Republic of China
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Hyart T, Mattas J, Alekseev KN. Model of the influence of an external magnetic field on the gain of terahertz radiation from semiconductor superlattices. PHYSICAL REVIEW LETTERS 2009; 103:117401. [PMID: 19792399 DOI: 10.1103/physrevlett.103.117401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2009] [Indexed: 05/28/2023]
Abstract
We theoretically analyze the influence of magnetic field on small-signal absorption and gain in a superlattice. We predict a very large and tunable THz gain due to nonlinear cyclotron oscillations in crossed electric and magnetic fields. In contrast to Bloch gain, here the superlattice is in an electrically stable state. We also find that THz Bloch gain can be significantly enhanced with a perpendicular magnetic field. If the magnetic field is tilted with respect to the superlattice axis, the usually unstable Bloch gain profile becomes stable in the vicinity of Stark-cyclotron resonances.
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Affiliation(s)
- Timo Hyart
- Department of Physics, P. O. Box 3000, FI-90014 University of Oulu, Oulu, Finland
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Huang L, Lai YC, Ferry DK, Goodnick SM, Akis R. Relativistic quantum scars. PHYSICAL REVIEW LETTERS 2009; 103:054101. [PMID: 19792502 DOI: 10.1103/physrevlett.103.054101] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2009] [Indexed: 05/28/2023]
Abstract
The concentrations of wave functions about classical periodic orbits, or quantum scars, are a fundamental phenomenon in physics. An open question is whether scarring can occur in relativistic quantum systems. To address this question, we investigate confinements made of graphene whose classical dynamics are chaotic and find unequivocal evidence of relativistic quantum scars. The scarred states can lead to strong conductance fluctuations in the corresponding open quantum dots via the mechanism of resonant transmission.
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Affiliation(s)
- Liang Huang
- Department of Electrical Engineering, Arizona State University, Tempe, Arizona 85287, USA
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Chen Z, Zhou W, Zhang B, Yu CH, Zhu J, Lu W, Shen SC. Realization of anisotropic diamagnetic kepler problem in a solid state environment. PHYSICAL REVIEW LETTERS 2009; 102:244103. [PMID: 19659011 DOI: 10.1103/physrevlett.102.244103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2009] [Indexed: 05/28/2023]
Abstract
The anisotropic diamagnetic Kepler problem (ADKP) is realized experimentally by the orbital electrons of a P donor in Si under magnetic fields. The interference of electron wave packets which leads to quasi-Landau resonances (QLR) were observed. Applying the closed-orbit theory to an anisotropic solid state environment, we have identified orbits responsible for the QLR manifesting the quantum chaotic behavior in Rydberg atoms. The excellent consistency between the measured spectra and theoretical calculation provides unambiguous evidence of quantum chaotic dynamics of electrons in the ADKP.
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Affiliation(s)
- Zhanghai Chen
- Surface Physics Laboratory, Department of Physics, Fudan University, Shanghai 200433, People's Republic of China.
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21
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Mullowney P, Julien K, Meiss JD. Chaotic advection and the emergence of tori in the Küppers-Lortz state. CHAOS (WOODBURY, N.Y.) 2008; 18:033104. [PMID: 19045442 DOI: 10.1063/1.2953575] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Motivated by the roll-switching behavior observed in rotating Rayleigh-Benard convection, we define a Küppers-Lortz (K-L) state as a volume-preserving flow with periodic roll switching. For an individual roll state, the Lagrangian particle trajectories are periodic. In a system with roll-switching, the particles can exhibit three-dimensional, chaotic motion. We study a simple phenomenological map that models the Lagrangian dynamics in a K-L state. When the roll axes differ by 120 degrees in the plane of rotation, we show that the phase space is dominated by invariant tori if the ratio of switching time to roll turnover time is small. When this parameter approaches zero these tori limit onto the classical hexagonal convection patterns, and, as it gets large, the dynamics becomes fully chaotic and well mixed. For intermediate values, there are interlinked toroidal and poloidal structures separated by chaotic regions. We also compute the exit time distributions and show that the unbounded chaotic orbits are normally diffusive. Although the map presumes instantaneous switching between roll states, we show that the qualitative features of the flow persist when the model has smooth, overlapping time-dependence for the roll amplitudes (the Busse-Heikes model).
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Affiliation(s)
- Paul Mullowney
- Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526, USA
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22
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Soskin SM, Mannella R, Yevtushenko OM. Matching of separatrix map and resonant dynamics, with application to global chaos onset between separatrices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:036221. [PMID: 18517499 DOI: 10.1103/physreve.77.036221] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2006] [Revised: 10/10/2007] [Indexed: 05/26/2023]
Abstract
We have developed a general method for the description of separatrix chaos, based on the analysis of the separatrix map dynamics. Matching it with the resonant Hamiltonian analysis, we show that, for a given amplitude of perturbation, the maximum width of the chaotic layer in energy may be much larger than it was assumed before. We use the above method to explain the drastic facilitation of global chaos onset in time-periodically perturbed Hamiltonian systems possessing two or more separatrices, previously discovered [S. M. Soskin, O. M. Yevtushenko, and R. Mannella, Phys. Rev. Lett. 90, 174101 (2003)]. The theory well agrees with simulations. We also discuss generalizations and applications. The method may be generalized for single-separatrix cases. The facilitation of global chaos onset may be relevant to a variety of systems, e.g., optical lattices, magnetic and semiconductor superlattices, meandering flows in the ocean, and spinning pendulums. Apart from dynamical transport, it may facilitate noise-induced transitions and the stochastic web formation.
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Affiliation(s)
- S M Soskin
- Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine
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Balanov AG, Fowler D, Patanè A, Eaves L, Fromhold TM. Bifurcations and chaos in semiconductor superlattices with a tilted magnetic field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:026209. [PMID: 18352105 DOI: 10.1103/physreve.77.026209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2007] [Revised: 10/30/2007] [Indexed: 05/26/2023]
Abstract
We study the effects of dissipation on electron transport in a semiconductor superlattice with an applied bias voltage and a magnetic field that is tilted relative to the superlattice axis. In previous work, we showed that, although the applied fields are stationary, they act like a terahertz plane wave, which strongly couples the Bloch and cyclotron motion of electrons within the lowest miniband. As a consequence, the electrons exhibit a unique type of Hamiltonian chaos, which creates an intricate mesh of conduction channels (a stochastic web) in phase space, leading to a large resonant increase in the current flow at critical values of the applied voltage. This phase-space patterning provides a sensitive mechanism for controlling electrical resistance. In this paper, we investigate the effects of dissipation on the electron dynamics by modifying the semiclassical equations of motion to include a linear damping term. We demonstrate that, even in the presence of dissipation, deterministic chaos plays an important role in the electron transport process. We identify mechanisms for the onset of chaos and explore the associated sequence of bifurcations in the electron trajectories. When the Bloch and cyclotron frequencies are commensurate, complex multistability phenomena occur in the system. In particular, for fixed values of the control parameters several distinct stable regimes can coexist, each corresponding to different initial conditions. We show that this multistability has clear, experimentally observable, signatures in the electron transport characteristics.
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Affiliation(s)
- A G Balanov
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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Abdullaev SS. Canonical stochastic web map. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:026216. [PMID: 17930130 DOI: 10.1103/physreve.76.026216] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2007] [Revised: 06/26/2007] [Indexed: 05/25/2023]
Abstract
In many Hamiltonian systems subjected to a time (or space) -periodic perturbation with a broad spectrum an approach is widely used of replacing the system by periodically delta -kicked dynamical systems, which allows us to reduce them to symplectic mappings. In this paper it is shown that this approach has a fundamental failure, and the corresponding mapping does not correctly describe the continuous original system. It is demonstrated on the example of the stochastic web map obtained by this approach to describe a periodically driven harmonic oscillator which exhibits non-Kolmogorov-Arnold-Moser chaos, particularly, the formation of stochastic webs. A correct canonical map corresponding to this system is obtained using a recently developed method based on the canonical transformation of variables [S. S. Abdullaev, J. Phys. A 35, 2811 (2002)]. Using a direct numerical integration of the system it is shown that the canonical map correctly describes the periodically driven harmonic oscillator with a finite number of spectrum modes.
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Affiliation(s)
- S S Abdullaev
- Institut für Energieforschung-Plasmaphysik, Forschungszentrum Jülich GmbH, EURATOM Association, Trilateral Euregio Cluster, D-52425 Jülich, Germany
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Hsueh WJ, Lin JC, Chen HC. Electronic minibands in complex basis superlattices: a numerically stable calculation. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2007; 19:266007. [PMID: 21694076 DOI: 10.1088/0953-8984/19/26/266007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
A numerically stable method for accurately determining the energy minibands of superlattices with arbitrary numbers of layers per cell is presented. Using a graph model with tangent and secant functions, we derive a set of concise and closed-form miniband edge equations for determining the miniband structure using topology theory. With the present method, it is not necessary to calculate the cosine of the Bloch phase, which may show a numerical overflow in calculation. Numerical results show that use of the miniband edge equations has better numerical stability than traditional methods in calculating the minibands of complex basis superlattices.
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Affiliation(s)
- W J Hsueh
- Department of Engineering Science, National Taiwan University, 1, Section 4, Roosevelt Road, Taipei 10660, Taiwan
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Brunner R, Meisels R, Kuchar F, Akis R, Ferry DK, Bird JP. Draining of the sea of chaos: role of resonant transmission and reflection in an array of billiards. PHYSICAL REVIEW LETTERS 2007; 98:204101. [PMID: 17677700 DOI: 10.1103/physrevlett.98.204101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2006] [Indexed: 05/16/2023]
Abstract
We investigate the dynamics of a system of coupled electron billiards by using a magnetic field to dramatically modify the underlying mixed phase space. At specific values of the magnetic field the sea of chaos is drained. At these fields there exist reflected or transmitted orbits associated with maxima and minima in the experimentally observed magnetoresistance. These effects are studied by comparing the classical and quantum-mechanical phase-space dynamics leading to a basic understanding of the role of chaos in the transport in an array of billiards.
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Affiliation(s)
- R Brunner
- Institute of Physics, University of Leoben, A-8700 Leoben, Austria
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27
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Patanè A, Fromhold M. Novel regimes of electron dynamics in superlattices. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2006; 364:3477-92. [PMID: 17090471 DOI: 10.1098/rsta.2006.1886] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
A superlattice (SL) is an artificial crystal in which alternating nanometre-thick layers of two or more different semiconductor materials provide a periodic potential for conduction electrons. Strong magnetic and electric fields applied to this type of structure provide a means of exploring novel regimes of electron dynamics. The applied fields lower the dimensionality of the electronic states and lead to qualitative changes in the electronic conduction. This discovery is of fundamental interest and highly relevant to the properties of other low-dimensional conductors, such as nanowires and quantum dot SLs, which are presently attracting the attention of the physics and device communities. In addition, a rare type of chaotic electron dynamics, called non-Kolmogorov-Arnold-Moser (KAM) chaotic motion, which has been theoretically studied for several decades, is observed experimentally in SLs. The onset of chaos at discrete values of the applied electric and magnetic fields is observed as a large increase in the current flow due to the creation of unbound electron orbits, which propagate through intricate web patterns in phase space. Therefore, non-KAM chaos could provide a new mechanism for controlling the electrical conductivity of the electronic devices with extreme sensitivity.
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Affiliation(s)
- Amalia Patanè
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK.
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28
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Buchleitner A, d'Arcy MB, Fishman S, Gardiner SA, Guarneri I, Ma ZY, Rebuzzini L, Summy GS. Quantum accelerator modes from the Farey tree. PHYSICAL REVIEW LETTERS 2006; 96:164101. [PMID: 16712235 DOI: 10.1103/physrevlett.96.164101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2005] [Indexed: 05/09/2023]
Abstract
We show that mode locking finds a purely quantum nondissipative counterpart in atom-optical quantum accelerator modes. These modes are formed by exposing cold atoms to periodic kicks in the direction of the gravitational field. They are anchored to generalized Arnol'd tongues, parameter regions where driven nonlinear classical systems exhibit mode locking. A hierarchy for the rational numbers known as the Farey tree provides an ordering of the Arnol'd tongues and hence of experimentally observed accelerator modes.
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Affiliation(s)
- A Buchleitner
- Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany
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29
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Kosevich YA, Hummel AB, Roskos HG, Köhler K. Ultrafast Fiske effect in semiconductor superlattices. PHYSICAL REVIEW LETTERS 2006; 96:137403. [PMID: 16712033 DOI: 10.1103/physrevlett.96.137403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2005] [Indexed: 05/09/2023]
Abstract
The current flowing across a semiconductor superlattice in tilted electric and magnetic fields is known to exhibit resonant enhancement, when Landau states of neighboring wells align at certain ratios of the field strengths. We show that the ultrafast version of this effect, in which coherent electron wave packets are involved, has a profound analogy to the Fiske effect in superconductor Josephson junctions and superfluid weak links, in that the coupling of the tunneling-induced charge oscillations (magneto-Bloch versus Josephson oscillations) to another oscillator (in-plane cyclotron oscillations versus external oscillator modes) opens an elastic rectifying transport channel. We explore the superlattice effect both theoretically and experimentally, and find that the transient self-induced current can be adequately modeled if the damping of both types of coupled electron oscillations is properly taken into account.
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Affiliation(s)
- Yuriy A Kosevich
- N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, 119991 Moscow, Russia.
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30
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Ponomarev AV, Madroñero J, Kolovsky AR, Buchleitner A. Atomic current across an optical lattice. PHYSICAL REVIEW LETTERS 2006; 96:050404. [PMID: 16486908 DOI: 10.1103/physrevlett.96.050404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2005] [Indexed: 05/06/2023]
Abstract
We devise a microscopic model for the emergence of a collision-induced, fermionic atomic current across a tilted optical lattice. Tuning the--experimentally controllable--parameters of the microscopic dynamics allows us to switch from Ohmic to negative differential conductance.
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Affiliation(s)
- Alexey V Ponomarev
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
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31
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Segal D, Král P, Shapiro M. Reentrant onset of chaos in tubular image states. J Chem Phys 2005; 122:134705. [PMID: 15847487 DOI: 10.1063/1.1865932] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the reentrant onset of chaos in "tubular image states," which are loosely bound states of electrons formed in the vicinity (20-40 nm) of conducting nanotubes. Chaos is shown to arise when an electron is placed in the vicinity of two metallic nanotubess with a magnetic field applied along the tubes. At stronger magnetic fields B approximately 10 T, we observe the formation of Landau-like states encircling the two-tube system, which wipe out the chaos. We can reinstall the chaos by charging oppositely the nanotubes, thus breaking the symmetry of the system and correspondingly the shape of the Landau-like states. Detailed analysis of the onset of chaos is done by studying the statistical properties of the eigenvalues spectrum and by investigating the spatial autocorrelation functions of individual eigenstates.
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Affiliation(s)
- Dvira Segal
- Department of Chemical Physics, Weizmann Institute of Science, 76100 Rehovot, Israel
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32
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Carvalho ARR, Buchleitner A. Web-assisted tunneling in the kicked harmonic oscillator. PHYSICAL REVIEW LETTERS 2004; 93:204101. [PMID: 15600927 DOI: 10.1103/physrevlett.93.204101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2004] [Indexed: 05/24/2023]
Abstract
We show that heating of harmonically trapped ions by periodic delta kicks is dramatically enhanced at isolated values of the Lamb-Dicke parameter. At these values, quasienergy eigenstates localized on island structures undergo avoided crossings with extended web states.
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Affiliation(s)
- André R R Carvalho
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
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