1
|
Savin AV, Dmitriev SV. Influence of the internal degrees of freedom of coronene molecules on the nonlinear dynamics of a columnar chain. Phys Rev E 2023; 107:054216. [PMID: 37329037 DOI: 10.1103/physreve.107.054216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2023] [Accepted: 04/29/2023] [Indexed: 06/18/2023]
Abstract
The nonlinear dynamics of a one-dimensional molecular crystal in the form of a chain of planar coronene molecules is analyzed. Using molecular dynamics, it is shown that a chain of coronene molecules supports acoustic solitons, rotobreathers, and discrete breathers. An increase in the size of planar molecules in a chain leads to an increase in the number of internal degrees of freedom. This results in an increase in the rate of emission of phonons from spatially localized nonlinear excitations and a decrease in their lifetime. Presented results contribute to the understanding of the effect of the rotational and internal vibrational modes of molecules on the nonlinear dynamics of molecular crystals.
Collapse
Affiliation(s)
- Alexander V Savin
- Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow 119991, Russia
- Plekhanov Russian University of Economics, Moscow 117997, Russia
| | - Sergey V Dmitriev
- Institute of Molecule and Crystal Physics, Ufa Federal Research Centre of Russian Academy of Sciences, Oktyabrya Ave. 151, 450075 Ufa, Russia
- Ufa State Petroleum Technological University, Kosmonavtov St. 1, 450062 Ufa, Russia
| |
Collapse
|
2
|
Zhang AX, Hu XW, Jiang YF, Liang JC, Zhang Y, Zhang W, Xue JK. Localization and spin dynamics of spin-orbit-coupled Bose-Einstein condensates in deep optical lattices. Phys Rev E 2021; 104:064215. [PMID: 35030834 DOI: 10.1103/physreve.104.064215] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2021] [Accepted: 12/09/2021] [Indexed: 11/07/2022]
Abstract
We analytically and numerically discuss the dynamics of two pseudospin components Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) in deep optical lattices. Rich localized phenomena, such as breathers, solitons, self-trapping, and diffusion, are revealed and strongly depend on the strength of the atomic interaction, SOC, Raman detuning, and the spin polarization (i.e., the initial population difference of atoms between the two pseudospin components of BECs). The critical conditions for the transition of localized states are derived analytically. Based on the critical conditions, the detailed dynamical phase diagram describing the different dynamical regimes is derived. When the Raman detuning satisfies a critical condition, localized states with a fixed initial spin polarization can be observed. When the critical condition is not satisfied, we use two quenching methods, i.e., suddenly and linearly quenching Raman detuning from the soliton or breather state, to discuss the spin dynamics, phase transition, and wave packet dynamics by numerical simulation. The sudden quenching results in a damped oscillation of spin polarization and transforms the system to a new polarized state. Interestingly, the linear quenching of Raman detuning induces a controllable phase transition from an unpolarized phase to an expected polarized phase, while the soliton or breather dynamics is maintained.
Collapse
Affiliation(s)
- Ai-Xia Zhang
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Xiao-Wen Hu
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Yan-Fang Jiang
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Jun-Cheng Liang
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Ying Zhang
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Wei Zhang
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Ju-Kui Xue
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| |
Collapse
|
3
|
Bai XD, Malomed BA, Deng FG. Unidirectional transport of wave packets through tilted discrete breathers in nonlinear lattices with asymmetric defects. Phys Rev E 2016; 94:032216. [PMID: 27739723 DOI: 10.1103/physreve.94.032216] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2016] [Indexed: 11/07/2022]
Abstract
We consider the transfer of lattice wave packets through a tilted discrete breather (TDB) in opposite directions in the discrete nonlinear Schrödinger model with asymmetric defects, which may be realized as a Bose-Einstein condensate trapped in a deep optical lattice, or as optical beams in a waveguide array. A unidirectional transport mode is found, in which the incident wave packets, whose energy belongs to a certain interval between full reflection and full passage regions, pass the TDB only in one direction, while in the absence of the TDB, the same lattice admits bidirectional propagation. The operation of this mode is accurately explained by an analytical consideration of the respective energy barriers. The results suggest that the TDB may emulate the unidirectional propagation of atomic and optical beams in various settings. In the case of the passage of the incident wave packet, the scattering TDB typically shifts by one lattice unit in the direction from which the wave packet arrives, which is an example of the tractor-beam effect, provided by the same system, in addition to the rectification of incident waves.
Collapse
Affiliation(s)
- Xiao-Dong Bai
- Department of Physics and Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel.,Laboratory of Nonlinear-Optical Informatics, ITMO University, St. Petersburg 197101, Russia
| | - Fu-Guo Deng
- Department of Physics and Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
| |
Collapse
|
4
|
Hennig H, Neff T, Fleischmann R. Dynamical phase diagram of Gaussian wave packets in optical lattices. Phys Rev E 2016; 93:032219. [PMID: 27078356 DOI: 10.1103/physreve.93.032219] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2013] [Indexed: 11/07/2022]
Abstract
We study the dynamics of self-trapping in Bose-Einstein condensates (BECs) loaded in deep optical lattices with Gaussian initial conditions, when the dynamics is well described by the discrete nonlinear Schrödinger equation (DNLSE). In the literature an approximate dynamical phase diagram based on a variational approach was introduced to distinguish different dynamical regimes: diffusion, self-trapping, and moving breathers. However, we find that the actual DNLSE dynamics shows a completely different diagram than the variational prediction. We calculate numerically a detailed dynamical phase diagram accurately describing the different dynamical regimes. It exhibits a complex structure that can readily be tested in current experiments in BECs in optical lattices and in optical waveguide arrays. Moreover, we derive an explicit theoretical estimate for the transition to self-trapping in excellent agreement with our numerical findings, which may be a valuable guide as well for future studies on a quantum dynamical phase diagram based on the Bose-Hubbard Hamiltonian.
Collapse
Affiliation(s)
- H Hennig
- Max Planck Institute for Dynamics and Self-Organization, 37073 Göttingen, Germany.,Department of Physics, Harvard University, Cambridge, Massachesetts 02138, USA
| | - T Neff
- Max Planck Institute for Dynamics and Self-Organization, 37073 Göttingen, Germany
| | - R Fleischmann
- Max Planck Institute for Dynamics and Self-Organization, 37073 Göttingen, Germany
| |
Collapse
|
5
|
Bai XD, Zhang M, Xiong J, Yang GJ, Deng FG. Selective distillation phenomenon in two-species Bose-Einstein condensates in open boundary optical lattices. Sci Rep 2015; 5:17101. [PMID: 26597592 PMCID: PMC4656982 DOI: 10.1038/srep17101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2015] [Accepted: 10/26/2015] [Indexed: 11/30/2022] Open
Abstract
We investigate the formation of discrete breathers (DBs) and the dynamics of the mixture of two-species Bose-Einstein condensates (BECs) in open boundary optical lattices using the discrete nonlinear Schrödinger equations. The results show that the coupling of intra- and interspecies interaction can lead to the existence of pure single-species DBs and symbiotic DBs (i.e., two-species DBs). Furthermore, we find that there is a selective distillation phenomenon in the dynamics of the mixture of two-species BECs. One can selectively distil one species from the mixture of two-species BECs and can even control dominant species fraction by adjusting the intra- and interspecies interaction in optical lattices. Our selective distillation mechanism may find potential application in quantum information storage and quantum information processing based on multi-species atoms.
Collapse
Affiliation(s)
- Xiao-Dong Bai
- Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
| | - Mei Zhang
- Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
| | - Jun Xiong
- Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
| | - Guo-Jian Yang
- Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
| | - Fu-Guo Deng
- Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
| |
Collapse
|
6
|
Balachandran B, Perkins E, Fitzgerald T. Response localization in micro-scale oscillator arrays: influence of cubic coupling nonlinearities. ACTA ACUST UNITED AC 2014. [DOI: 10.1007/s40435-014-0139-9] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
7
|
Bai XD, Zhang AX, Xue JK. Transfer of dipolar gas through the discrete localized mode. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062916. [PMID: 24483540 DOI: 10.1103/physreve.88.062916] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2013] [Indexed: 06/03/2023]
Abstract
By considering the discrete nonlinear Schrödinger model with dipole-dipole interactions for dipolar condensate, the existence, the types, the stability, and the dynamics of the localized modes in a nonlinear lattice are discussed. It is found that the contact interaction and the dipole-dipole interactions play important roles in determining the existence, the type, and the stability of the localized modes. Because of the coupled effects of the contact interaction and the dipole-dipole interactions, rich localized modes and their stability nature can exist: when the contact interaction is larger and the dipole-dipole interactions is smaller, a discrete bright breather occurs. In this case, while the on-site interaction can stabilize the discrete breather, the dipole-dipole interactions will destabilize the discrete breather; when both the contact interaction and the dipole-dipole interactions are larger, a discrete kink appears. In this case, both the on-site interaction and the dipole-dipole interactions can stabilize the discrete kink, but the discrete kink is more unstable than the ordinary discrete breather. The predicted results provide a deep insight into the dynamics of blocking, filtering, and transfer of the norm in nonlinear lattices for dipolar condensates.
Collapse
Affiliation(s)
- Xiao-Dong Bai
- Key Laboratory of Atomic & Molecular Physics and Functional Materials of Gansu Province, College of Physics and Electronics Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Ai-Xia Zhang
- Key Laboratory of Atomic & Molecular Physics and Functional Materials of Gansu Province, College of Physics and Electronics Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Ju-Kui Xue
- Key Laboratory of Atomic & Molecular Physics and Functional Materials of Gansu Province, College of Physics and Electronics Engineering, Northwest Normal University, Lanzhou 730070, China
| |
Collapse
|
8
|
English LQ, Palmero F, Stormes JF, Cuevas J, Carretero-González R, Kevrekidis PG. Nonlinear localized modes in two-dimensional electrical lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022912. [PMID: 24032906 DOI: 10.1103/physreve.88.022912] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2013] [Revised: 05/15/2013] [Indexed: 06/02/2023]
Abstract
We report the observation of spontaneous localization of energy in two spatial dimensions in the context of nonlinear electrical lattices. Both stationary and moving self-localized modes were generated experimentally and theoretically in a family of two-dimensional square as well as honeycomb lattices composed of 6 × 6 elements. Specifically, we find regions in driver voltage and frequency where stationary discrete breathers, also known as intrinsic localized modes (ILMs), exist and are stable due to the interplay of damping and spatially homogeneous driving. By introducing additional capacitors into the unit cell, these lattices can controllably induce mobile discrete breathers. When more than one such ILMs are experimentally generated in the lattice, the interplay of nonlinearity, discreteness, and wave interactions generates a complex dynamics wherein the ILMs attempt to maintain a minimum distance between one another. Numerical simulations show good agreement with experimental results and confirm that these phenomena qualitatively carry over to larger lattice sizes.
Collapse
Affiliation(s)
- L Q English
- Department of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA
| | | | | | | | | | | |
Collapse
|
9
|
Sato M, Imai S, Fujita N, Shi W, Takao Y, Sada Y, Hubbard BE, Ilic B, Sievers AJ. Switching dynamics and linear response spectra of a driven one-dimensional nonlinear lattice containing an intrinsic localized mode. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012920. [PMID: 23410417 DOI: 10.1103/physreve.87.012920] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2012] [Revised: 12/16/2012] [Indexed: 06/01/2023]
Abstract
An intrinsic localized mode (ILM) represents a localized vibrational excitation in a nonlinear lattice. Such a mode will stay in resonance as the driver frequency is changed adiabatically until a bifurcation point is reached, at which point the ILM switches and disappears. The dynamics behind switching in such a many body system is examined here through experimental measurements and numerical simulations. Linear response spectra of a driven micromechanical array containing an ILM were measured in the frequency region between two fundamentally different kinds of bifurcation points that separate the large amplitude ILM state from the two low amplitude vibrational states. Just as a natural frequency can be associated with a driven harmonic oscillator, a similar natural frequency has been found for a driven ILM via the beat frequency between it and a weak, tunable probe. This finding has been confirmed using numerical simulations. The behavior of this nonlinear natural frequency plays important but different roles as the two bifurcation points are approached. At the upper transition its frequency coalesces with the driver and the resulting bifurcation is very similar to the saddle-node bifurcation of a single driven Duffing oscillator, which is treated in an Appendix. The lower transition occurs when the four-wave mixing partner of the natural frequency of the ILM intersects the topmost extended band mode of the same symmetry. The properties of linear local modes associated with the driven ILM are also identified experimentally for the first time and numerically but play no role in these transitions.
Collapse
Affiliation(s)
- M Sato
- Graduate School of Natural Science and Technology, Kanazawa University Kanazawa, Ishikawa 920-1192, Japan.
| | | | | | | | | | | | | | | | | |
Collapse
|
10
|
Bai XD, Xue JK. Discrete breather and its stability in a general discrete nonlinear Schrödinger equation with disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:066605. [PMID: 23368070 DOI: 10.1103/physreve.86.066605] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2012] [Revised: 12/05/2012] [Indexed: 06/01/2023]
Abstract
By considering a general discrete nonlinear Schrödinger model with arbitrary values of nonlinearity power and disorder, the existence and stability of a discrete breather (DB) in a general nonlinear lattice are discussed. It is found that nonlinearity and disorder play important roles in determining the existence and stability of the DB. Nonlinearity (expressed by the interparticle interaction) and disorder can enhance the stability of the DB. Remarkably, we find that the DB is most stable when the nonlinearity power is equal to a critical value. The effects of nonlinearity, nonlinearity power, and disorder on the stability of the DB are strongly coupled.
Collapse
Affiliation(s)
- Xiao-Dong Bai
- Key Laboratory of Atomic & Molecular Physics and Functional Materials of Gansu Province, College of Physics and Electronics Engineering, Northwest Normal University, Lanzhou 730070, China
| | | |
Collapse
|
11
|
English LQ, Palmero F, Sievers AJ, Kevrekidis PG, Barnak DH. Traveling and stationary intrinsic localized modes and their spatial control in electrical lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:046605. [PMID: 20481851 DOI: 10.1103/physreve.81.046605] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2010] [Indexed: 05/29/2023]
Abstract
This work focuses on the production of both stationary and traveling intrinsic localized modes (ILMs), also known as discrete breathers, in two closely related electrical lattices; we demonstrate experimentally that the interplay between these two ILM types can be utilized for the purpose of spatial control. We describe a novel mechanism that is responsible for the motion of driven ILMs in this system, and quantify this effect by modeling in some detail the electrical components comprising the lattice.
Collapse
Affiliation(s)
- L Q English
- Deptartment of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA
| | | | | | | | | |
Collapse
|
12
|
Sarkar R, Dey B. Dynamics of a curved Fermi-Pasta-Ulam chain: effects of geometry, long-range interaction, and nonlinear dispersion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:016605. [PMID: 17677583 DOI: 10.1103/physreve.76.016605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2006] [Revised: 05/30/2007] [Indexed: 05/16/2023]
Abstract
We study the dynamics of the bent Fermi-Pasta-Ulam (FPU) chain, incorporating the complicated effects of geometry, long-range interactions, as well as nonlinear dispersion. Within the rotating wave approximation, we obtain several exact discrete breather (DB) solutions, such as the odd-parity and even-parity discrete breathers, compactlike discrete breathers and moving discrete breathers for various geometries of the chain. In presence of long-range nonlinear dispersive interactions, we show that DBs exist in the discrete curved lattice for next-nearest-neighbor interactions as well. For all neighbors interactions, we treat the problem in the long-wavelength (continuum) and weakly nonlinear limit of the system and obtain exact static breather solutions and large-amplitude, traveling kink-soliton solutions. The curved FPU chain also admits finite amplitude discrete nonlinear sinusoidal wave solutions with short commensurate as well as incommensurate wavelengths. The usefulness of these solutions for energy localization and transport in various physical systems are discussed.
Collapse
Affiliation(s)
- Ranja Sarkar
- Department of Physics, University of Pune, Pune-411007, India
| | | |
Collapse
|
13
|
Molina MI. Nonlinear surface impurity in a semi-infinite two-dimensional square lattice: Green function approach. PHYSICAL REVIEW B 2006; 74:045412. [DOI: 10.1103/physrevb.74.045412] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
|
14
|
Flach S, Gorbach A. Discrete breathers in Fermi-Pasta-Ulam lattices. CHAOS (WOODBURY, N.Y.) 2005; 15:15112. [PMID: 15836289 DOI: 10.1063/1.1839151] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We study the properties of spatially localized and time-periodic excitations--discrete breathers--in Fermi-Pasta-Ulam (FPU) chains. We provide a detailed analysis of their spatial profiles and stability properties. We especially demonstrate that the Page mode is linearly stable for symmetric FPU potentials. A resonant interaction between a localized and delocalized perturbations causes weak but finite strength instabilities for asymmetric FPU potentials. This interaction induces Fano resonances for plane waves scattered by the breather. Finally we analyze the interplay between energy thresholds for breathers in the presence of strongly asymmetric FPU potentials and the corresponding profiles of the low-frequency limit of breather families.
Collapse
Affiliation(s)
- S Flach
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
| | | |
Collapse
|