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Jiao Y, Zeng C, Luo Y. Roughness induced current reversal in fractional hydrodynamic memory. CHAOS (WOODBURY, N.Y.) 2023; 33:093140. [PMID: 37748483 DOI: 10.1063/5.0164625] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2023] [Accepted: 09/07/2023] [Indexed: 09/27/2023]
Abstract
The existence of a corrugated surface is of great importance and ubiquity in biological systems, exhibiting diverse dynamic behaviors. However, it has remained unclear whether such rough surface leads to the current reversal in fractional hydrodynamic memory. We investigate the transport of a particle within a rough potential under external forces in a subdiffusive media with fractional hydrodynamic memory. The results demonstrate that roughness induces current reversal and a transition from no transport to transport. These phenomena are analyzed through the subdiffusion, Peclet number, useful work, input power, and thermodynamic efficiency. The analysis reveals that transport results from energy conversion, wherein time-dependent periodic force is partially converted into mechanical energy to drive transport against load, and partially dissipated through environmental absorption. In addition, the findings indicate that the size and shape of ratchet tune the occurrence and disappearance of the current reversal, and control the number of times of the current reversal occurring. Furthermore, we find that temperature, friction, and load tune transport, resonant-like activity, and enhanced stability of the system, as evidenced by thermodynamic efficiency. These findings may have implications for understanding dynamics in biological systems and may be relevant for applications involving molecular devices for particle separation at the mesoscopic scale.
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Affiliation(s)
- Yuanyuan Jiao
- Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
| | - Chunhua Zeng
- Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
| | - Yuhui Luo
- School of Physics and Information Engineering, Zhaotong University, Zhaotong 657000, China
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2
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Marchenko IG, Aksenova V, Marchenko II, Łuczka J, Spiechowicz J. Temperature anomalies of oscillating diffusion in ac-driven periodic systems. Phys Rev E 2023; 107:064116. [PMID: 37464623 DOI: 10.1103/physreve.107.064116] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Accepted: 06/02/2023] [Indexed: 07/20/2023]
Abstract
We analyze the impact of temperature on the diffusion coefficient of an inertial Brownian particle moving in a symmetric periodic potential and driven by a symmetric time-periodic force. Recent studies have revealed the low-friction regime in which the diffusion coefficient shows giant damped quasiperiodic oscillations as a function of the amplitude of the time-periodic force [I. G. Marchenko et al., Chaos 32, 113106 (2022)1054-150010.1063/5.0117902]. We find out that when temperature grows the diffusion coefficient increases at its minima; however, it decreases at the maxima within a finite temperature window. This curious behavior is explained in terms of the deterministic dynamics perturbed by thermal fluctuations and mean residence time of the particle in the locked and running trajectories. We demonstrate that temperature dependence of the diffusion coefficient can be accurately reconstructed from the stationary probability to occupy the running trajectories.
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Affiliation(s)
- I G Marchenko
- NSC Kharkiv Institute of Physics and Technology, Kharkiv 61108, Ukraine
- Karazin Kharkiv National University, Kharkiv 61022, Ukraine
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - V Aksenova
- NSC Kharkiv Institute of Physics and Technology, Kharkiv 61108, Ukraine
- Karazin Kharkiv National University, Kharkiv 61022, Ukraine
| | - I I Marchenko
- NTU Kharkiv Polytechnic Institute, Kharkiv 61002, Ukraine
| | - J Łuczka
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - J Spiechowicz
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
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3
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Wiśniewski M, Spiechowicz J. Paradoxical nature of negative mobility in the weak dissipation regime. CHAOS (WOODBURY, N.Y.) 2023; 33:2894479. [PMID: 37276563 DOI: 10.1063/5.0146649] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 05/02/2023] [Indexed: 06/07/2023]
Abstract
We reinvestigate a paradigmatic model of nonequilibrium statistical physics consisting of an inertial Brownian particle in a symmetric periodic potential subjected to both a time-periodic force and a static bias. In doing so, we focus on the negative mobility phenomenon in which the average velocity of the particle is opposite to the constant force acting on it. Surprisingly, we find that in the weak dissipation regime, thermal fluctuations induce negative mobility much more frequently than it happens if dissipation is stronger. In particular, for the very first time, we report a parameter set in which thermal noise causes this effect in the nonlinear response regime. Moreover, we show that the coexistence of deterministic negative mobility and chaos is routinely encountered when approaching the overdamped limit in which chaos does not emerge rather than near the Hamiltonian regime of which chaos is one of the hallmarks. On the other hand, at non-zero temperature, the negative mobility in the weak dissipation regime is typically affected by weak ergodicity breaking. Our findings can be corroborated experimentally in a multitude of physical realizations, including, e.g., Josephson junctions and cold atoms dwelling in optical lattices.
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Affiliation(s)
- Mateusz Wiśniewski
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
| | - Jakub Spiechowicz
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
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4
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Białas K, Łuczka J, Spiechowicz J. Periodic potential can enormously boost free-particle transport induced by active fluctuations. Phys Rev E 2023; 107:024107. [PMID: 36932589 DOI: 10.1103/physreve.107.024107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Accepted: 01/20/2023] [Indexed: 06/18/2023]
Abstract
Active fluctuations are detected in a growing number of systems due to self-propulsion mechanisms or collisions with an active environment. They drive the system far from equilibrium and can induce phenomena that are forbidden at equilibrium states by, e.g., fluctuation-dissipation relations and detailed balance symmetry. Understanding their role in living matter is emerging as a challenge for physics. Here we demonstrate a paradoxical effect in which a free-particle transport induced by active fluctuations can be boosted by many orders of magnitude when the particle is additionally subjected to a periodic potential. In contrast, within the realm of only thermal fluctuations, the velocity of a free particle exposed to a bias is reduced when the periodic potential is switched on. The presented mechanism is significant for understanding nonequilibrium environments such as living cells, where it can explain from a fundamental point of view why spatially periodic structures known as microtubules are necessary to generate impressively effective intracellular transport. Our findings can be readily corroborated experimentally, e.g., in a setup comprising a colloidal particle in an optically generated periodic potential.
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Affiliation(s)
- K Białas
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - J Łuczka
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - J Spiechowicz
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
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5
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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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6
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Marchenko IG, Zhiglo A, Aksenova V, Tkachenko V, Marchenko II, Łuczka J, Spiechowicz J. Giant oscillations of diffusion in ac-driven periodic systems. CHAOS (WOODBURY, N.Y.) 2022; 32:113106. [PMID: 36456332 DOI: 10.1063/5.0117902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
We revisit the problem of diffusion in a driven system consisting of an inertial Brownian particle moving in a symmetric periodic potential and subjected to a symmetric time-periodic force. We reveal parameter domains in which diffusion is normal in the long time limit and exhibits intriguing giant damped quasiperiodic oscillations as a function of the external driving amplitude. As the mechanism behind this effect, we identify the corresponding oscillations of difference in the number of locked and running trajectories that carry the leading contribution to the diffusion coefficient. Our findings can be verified experimentally in a multitude of physical systems, including colloidal particles, Josephson junction, or cold atoms dwelling in optical lattices, to name only a few.
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Affiliation(s)
- I G Marchenko
- NSC "Kharkiv Institute of Physics and Technology," Kharkiv 61108, Ukraine
| | - A Zhiglo
- NSC "Kharkiv Institute of Physics and Technology," Kharkiv 61108, Ukraine
| | - V Aksenova
- NSC "Kharkiv Institute of Physics and Technology," Kharkiv 61108, Ukraine
| | - V Tkachenko
- NSC "Kharkiv Institute of Physics and Technology," Kharkiv 61108, Ukraine
| | - I I Marchenko
- NTU "Kharkiv Polytechnic Institute," Kharkiv 61145, Ukraine
| | - J Łuczka
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - J Spiechowicz
- NTU "Kharkiv Polytechnic Institute," Kharkiv 61145, Ukraine
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7
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Velocity Multistability vs. Ergodicity Breaking in a Biased Periodic Potential. ENTROPY 2022; 24:e24010098. [PMID: 35052124 PMCID: PMC8774412 DOI: 10.3390/e24010098] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/16/2021] [Revised: 01/04/2022] [Accepted: 01/05/2022] [Indexed: 11/17/2022]
Abstract
Multistability, i.e., the coexistence of several attractors for a given set of system parameters, is one of the most important phenomena occurring in dynamical systems. We consider it in the velocity dynamics of a Brownian particle, driven by thermal fluctuations and moving in a biased periodic potential. In doing so, we focus on the impact of ergodicity-A concept which lies at the core of statistical mechanics. The latter implies that a single trajectory of the system is representative for the whole ensemble and, as a consequence, the initial conditions of the dynamics are fully forgotten. The ergodicity of the deterministic counterpart is strongly broken, and we discuss how the velocity multistability depends on the starting position and velocity of the particle. While for non-zero temperatures the ergodicity is, in principle, restored, in the low temperature regime the velocity dynamics is still affected by initial conditions due to weak ergodicity breaking. For moderate and high temperatures, the multistability is robust with respect to the choice of the starting position and velocity of the particle.
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Białas K, Spiechowicz J. Colossal Brownian yet non-Gaussian diffusion in a periodic potential: Impact of nonequilibrium noise amplitude statistics. CHAOS (WOODBURY, N.Y.) 2021; 31:123107. [PMID: 34972330 DOI: 10.1063/5.0068039] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2021] [Accepted: 11/13/2021] [Indexed: 06/14/2023]
Abstract
Last year, Białas et al. [Phys. Rev. E 102, 042121 (2020)] studied an overdamped dynamics of nonequilibrium noise driven Brownian particle dwelling in a spatially periodic potential and discovered a novel class of Brownian, yet non-Gaussian diffusion. The mean square displacement of the particle grows linearly with time and the probability density for the particle position is Gaussian; however, the corresponding distribution for the increments is non-Gaussian. The latter property induces the colossal enhancement of diffusion, significantly exceeding the well known effect of giant diffusion. Here, we considerably extend the above predictions by investigating the influence of nonequilibrium noise amplitude statistics on the colossal Brownian, yet non-Gaussian diffusion. The tail of amplitude distribution crucially impacts both the magnitude of diffusion amplification and the Gaussianity of the position and increments statistics. Our results carry profound consequences for diffusive behavior in nonequilibrium settings such as living cells in which diffusion is a central transport mechanism.
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Affiliation(s)
- K Białas
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - J Spiechowicz
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
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9
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Spiechowicz J, Łuczka J. Conundrum of weak-noise limit for diffusion in a tilted periodic potential. Phys Rev E 2021; 104:034104. [PMID: 34654194 DOI: 10.1103/physreve.104.034104] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2021] [Accepted: 08/20/2021] [Indexed: 11/07/2022]
Abstract
The weak-noise limit of dissipative dynamical systems is often the most fascinating one. In such a case fluctuations can interact with a rich complexity, frequently hidden in deterministic systems, to give rise to phenomena that are absent for both noiseless and strong fluctuations regimes. Unfortunately, this limit is also notoriously hard to approach analytically or numerically. We reinvestigate in this context the paradigmatic model of nonequilibrium statistical physics consisting of inertial Brownian particles diffusing in a tilted periodic potential by exploiting state-of-the-art computer simulations of an extremely long timescale. In contrast to previous results on this longstanding problem, we draw an inference that in the parameter regime for which the particle velocity is bistable the lifetime of ballistic diffusion diverges to infinity when the thermal noise intensity tends to zero, i.e., an everlasting ballistic diffusion emerges. As a consequence, the diffusion coefficient does not reach its stationary constant value.
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Affiliation(s)
- J Spiechowicz
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - J Łuczka
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
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10
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Collective transient ratchet transport induced by many elastically interacting particles. Sci Rep 2021; 11:16178. [PMID: 34376759 PMCID: PMC8355274 DOI: 10.1038/s41598-021-95654-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Accepted: 07/22/2021] [Indexed: 11/21/2022] Open
Abstract
Several dynamical systems in nature can be maintained out-of-equilibrium, either through mutual interaction of particles or by external fields. The particle’s transport and the transient dynamics are landmarking of such systems. While single ratchet systems are genuine candidates to describe unbiased transport, we demonstrate here that coupled ratchets exhibit collective transient ratchet transport. Extensive numerical simulations for up to \documentclass[12pt]{minimal}
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\begin{document}$$N=1024$$\end{document}N=1024 elastically interacting ratchets establish the generation of large transient ratchet currents (RCs). The lifetimes of the transient RCs increase with N and decrease with the coupling strength between the ratchets. We demonstrate one peculiar case having a coupling-induced transient RC through the asymmetric destruction of attractors. Results suggest that physical devices built with coupled ratchet systems should present large collective transient transport of particles, whose technological applications are undoubtedly appealing and feasible.
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Spiechowicz J, Łuczka J. Arcsine law and multistable Brownian dynamics in a tilted periodic potential. Phys Rev E 2021; 104:024132. [PMID: 34525677 DOI: 10.1103/physreve.104.024132] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2021] [Accepted: 08/10/2021] [Indexed: 06/13/2023]
Abstract
Multistability is one of the most important phenomena in dynamical systems, e.g., bistability enables the implementation of logic gates and therefore computation. Recently multistability has attracted a greatly renewed interest related to memristors and graphene structures, to name only a few. We investigate tristability in velocity dynamics of a Brownian particle subjected to a tilted periodic potential. It is demonstrated that the origin of this effect is attributed to the arcsine law for the velocity dynamics at the zero temperature limit. We analyze the impact of thermal fluctuations and construct the phase diagram for the stability of the velocity dynamics. It suggests an efficient strategy to control the multistability by changing solely the force acting on the particle or temperature of the system. Our findings for the paradigmatic model of nonequilibrium statistical physics apply to, inter alia, Brownian motors, Josephson junctions, cold atoms dwelling in optical lattices, and colloidal systems.
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Affiliation(s)
- J Spiechowicz
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - J Łuczka
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
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Słapik A, Spiechowicz J. Tunable particle separation via deterministic absolute negative mobility. Sci Rep 2020; 10:16639. [PMID: 33024188 PMCID: PMC7538438 DOI: 10.1038/s41598-020-73470-w] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2020] [Accepted: 08/31/2020] [Indexed: 11/17/2022] Open
Abstract
Particle isolation techniques are in the spotlight of many areas of science and engineering. In food industry, a harmful bacterial activity can be prevented with the help of separation schemes. In health care, isolation techniques are used to distinguish cancer and healthy cells or in therapy for Alzheimer's and Parkinson's diseases. We consider a cloud of Brownian particles of different sizes moving in a periodic potential and subjected to an unbiased driving as well as a constant force. We reveal an efficient separation strategy via the counterintuitive effect of negative mobility when particles of a given size are transported in a direction opposite to the applied constant force. We demonstrate a tunable separation solution in which size of the particle undergoing separation may be controlled by variation of the parameters of the external force applied to the system. This approach is an important step towards the development of point-of-care lab-on-a-chip devices.
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Affiliation(s)
- A Słapik
- Institute of Physics, University of Silesia, 40-007, Katowice, Poland
| | - J Spiechowicz
- Institute of Physics, University of Silesia, 40-007, Katowice, Poland.
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Spiechowicz J, Łuczka J. Diffusion in a biased washboard potential revisited. Phys Rev E 2020; 101:032123. [PMID: 32289947 DOI: 10.1103/physreve.101.032123] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2019] [Accepted: 03/03/2020] [Indexed: 06/11/2023]
Abstract
The celebrated Sutherland-Einstein relation for systems at thermal equilibrium states that spread of trajectories of Brownian particles is an increasing function of temperature. Here, we scrutinize the diffusion of underdamped Brownian motion in a biased periodic potential and analyze regimes in which a diffusion coefficient decreases with increasing temperature within a finite temperature window. Comprehensive numerical simulations of the corresponding Langevin equation performed with unprecedented resolution allow us to construct a phase diagram for the occurrence of the nonmonotonic temperature dependence of the diffusion coefficient. We discuss the relation of the later effect with the phenomenon of giant diffusion.
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Affiliation(s)
- J Spiechowicz
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - J Łuczka
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
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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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