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Wiśniewski M, Spiechowicz J. Memory-induced absolute negative mobility. CHAOS (WOODBURY, N.Y.) 2024; 34:073101. [PMID: 38949530 DOI: 10.1063/5.0213706] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2024] [Accepted: 06/10/2024] [Indexed: 07/02/2024]
Abstract
Non-Markovian systems form a broad area of physics that remains greatly unexplored despite years of intensive investigations. The spotlight is on memory as a source of effects that are absent in their Markovian counterparts. In this work, we dive into this problem and analyze a driven Brownian particle moving in a spatially periodic potential and exposed to correlated thermal noise. We show that the absolute negative mobility effect, in which the net movement of the particle is in the direction opposite to the average force acting on it, may be induced by the memory of the setup. To explain the origin of this phenomenon, we resort to the recently developed effective mass approach to dynamics of non-Markovian systems.
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Affiliation(s)
- M Wiśniewski
- 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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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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Lad KN, Patel MK, Pratap A. Brownian motion with time-dependent friction and single-particle dynamics in liquids. Phys Rev E 2022; 105:064107. [PMID: 35854483 DOI: 10.1103/physreve.105.064107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2022] [Accepted: 05/18/2022] [Indexed: 11/07/2022]
Abstract
A microscopic theory of molecular motion in classical monatomic liquids, proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)10.1103/PhysRev.176.239], is revisited and extended to incorporate the dynamic friction in the Brownian description of the atomic diffusion in a mean-time-dependent harmonic force field. A modified, non-Markovian Langevin equation is utilized to derive an equation of motion for the velocity autocorrelation function with time-dependent friction coefficient. Numerical solution of the equation gives an excellent account of the velocity autocorrelation function in Lennard-Jones liquids, liquid alkali, and transition metals over a broad range of density and temperature. Derivation of the equation of motion leads to a self-consistent expression for the time dependence of friction coefficient. Our results demonstrate that the nature of time dependence of the friction coefficient changes dramatically with the liquid density. At low and moderate densities, the dynamic friction decays exponentially whereas it increases exponentially at high liquid densities. Our findings provide an opportunity for a different outlook of the Brownian description of atomic dynamics in liquids.
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Affiliation(s)
- Kirit N Lad
- Computational Condensed Matter Physics Laboratory, Department of Physics, Sardar Patel University, Vallabh Vidya Nagar-388120, Gujarat, India
| | - Margi K Patel
- Condensed Matter Physics Laboratory, Applied Physics Department, Faculty of Technology & Engineering, The M. S. University of Baroda, Vadodara-390001, Gujarat, India
| | - Arun Pratap
- Condensed Matter Physics Laboratory, Applied Physics Department, Faculty of Technology & Engineering, The M. S. University of Baroda, Vadodara-390001, Gujarat, India
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Luo Y, Zeng C, Li B. Negative rectification and anomalous diffusion in nonlinear substrate potentials: Dynamical relaxation and information entropy. Phys Rev E 2022; 105:024204. [PMID: 35291109 DOI: 10.1103/physreve.105.024204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2021] [Accepted: 01/12/2022] [Indexed: 06/14/2023]
Abstract
We numerically investigate the rectification of the probability flux and dynamical relaxation of particles moving in a system with and without noise. The system, driven by two external forces, consists of two substrate potentials that have identical shapes and different potential barriers with different friction coefficients. The deterministic model exhibits the perfect rectification of the probability flux, ratchet effect, and the dependence of the unpredictability of the dynamics on basin of attraction. In contrast, the stochastic model displays that the rectification is sensitive to the temperature and an external bias. They can induce kinetic phase transitions between no transport and a finite net transport. These transitions lead to an unexpected phenomenon, called negative rectification. The results are analyzed through the corresponding time-dependent diffusion coefficient, information entropy (IE), etc. At a low temperature, anomalous diffusions occur in system. For the occurrence of the flux in certain parameter regimes, the larger the diffusion is, the smaller the corresponding IE is, and vice versa. We also present the selected parameter regimes for the emergence of the rectification and negative rectification. Additionally, we study the rectification of the interacting particles in the system and find that the flux may depend on the coupling strength and the number of the interacting particles, and that collective motions occur for the forward flux. Our work provides not only a way of the rectification for the transport of various particles (e.g., ions, electrons, photons, phonons, molecules, DNA chains, nanoswimmers, dust particles, etc.) in physics, chemistry, biology, and material science, but also a design of various circuits.
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Affiliation(s)
- Yuhui Luo
- Faculty of Civil Engineering and Mechanics/Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
- School of Physics and Information Engineering, Zhaotong University, Zhaotong 657000, China
| | - Chunhua Zeng
- Faculty of Civil Engineering and Mechanics/Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
| | - Baowen Li
- Paul M. Rady Department of Mechanical Engineering and Department of Physics, University of Colorado, Boulder, Colorado 80309-0427, USA
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Zhang C, Yang T, Qu SX. Impact of time delays and environmental noise on the extinction of a population dynamics model. THE EUROPEAN PHYSICAL JOURNAL. B 2021; 94:219. [PMID: 34751210 PMCID: PMC8565651 DOI: 10.1140/epjb/s10051-021-00219-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/29/2021] [Accepted: 09/27/2021] [Indexed: 06/13/2023]
Abstract
ABSTRACT In this paper, we examine a population model with carrying capacity, time delay, and sources of additive and multiplicative environmental noise. We find that time delay, noise sources and their correlation induce regime shifts and transitions between the population survival state and the extinction state. To explore the transition mechanism between these two states, we analyzed the shift time to extinction, or the delayed extinction time, of populations. The main finding is that the extinction transition time as a function of the noise intensity shows a maximum, indicating the existence of an appropriate noise intensity leading to a maximal delayed extinction. This nonmonotonic behavior, with a maximum, is a signature of the noise-enhanced stability phenomenon, observed in many physical and complex metastable systems. In particular, this maximum increases (or decreases) as the cross-correlation intensity or the delay time in the death process increases. Furthermore, the signal-to-noise ratio as a function of noise intensity shows a maximum, which is a signature of the stochastic resonance phenomenon in the population dynamics model investigated in the presence of time delay and environmental noise.
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Affiliation(s)
- Chun Zhang
- School of Physics and Information Technology, Shaanxi Normal University, Xi’an, 710062 People’s Republic of China
| | - Tao Yang
- Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an, 710072 People’s Republic of China
| | - Shi-Xian Qu
- School of Physics and Information Technology, Shaanxi Normal University, Xi’an, 710062 People’s Republic of China
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Xiong Z, Li X, Ye M, Zhang Q. Finite-time stability and optimal control of an impulsive stochastic reaction-diffusion vegetation-water system driven by Lévy process with time-varying delay. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:8462-8498. [PMID: 34814308 DOI: 10.3934/mbe.2021419] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
In this paper, a reaction-diffusion vegetation-water system with time-varying delay, impulse and Lévy jump is proposed. The existence and uniqueness of the positive solution are proved. Meanwhile, mainly through the principle of comparison, we obtain the sufficient conditions for finite-time stability which reflect the effect of time delay, diffusion, impulse, and noise. Besides, considering the planting, irrigation and other measures, we introduce control variable into the vegetation-water system. In order to save the costs of strategies, the optimal control is analyzed by using the minimum principle. Finally, numerical simulations are shown to illustrate the effectiveness of our theoretical results.
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Affiliation(s)
- Zixiao Xiong
- School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China
| | - Xining Li
- School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China
| | - Ming Ye
- Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA
- Department of Earth, Ocean, and Atmospheric Science, Florida State University, Tallahassee, FL 32306, USA
| | - Qimin Zhang
- School of Creative and Cultural Business, Robert Gordon University, Aberdeen, Scotland, UK
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Luo Y, Zeng C, Ai BQ. Strong-chaos-caused negative mobility in a periodic substrate potential. Phys Rev E 2020; 102:042114. [PMID: 33212680 DOI: 10.1103/physreve.102.042114] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2020] [Accepted: 09/17/2020] [Indexed: 01/23/2023]
Abstract
We numerically investigate negative mobility of an inertial Brownian particle moving in a periodic double-well substrate potential in the presence of a time-periodic force and a constant bias. For the deterministic case, we find from the average velocity that the varying shape parameter and driving forces can cause negative mobility, differential negative mobility, and giant positive mobility. We analyze these findings via the bifurcation diagram and maximal Lyapunov exponent and find that certain chaos can give rise to negative mobility. For the presence of a Gaussian color noise, the results suggest that the noise intensity can enhance or result in negative and positive mobilities, whereas correlation time can enhance, weaken, or even eliminate them. On the basis of the time series, phase-space map, and power spectrum of various attractors, we unveil how these mobilities connect to strong chaotic attractors (SCAs), including both stable attractor and unstable attractors, and propose an underlying mechanism that SCAs can result in the negative mobility, whereas other attractors do not. Our findings may be potentially useful for research on anomalous transports of the particles and on designs of various devices, such as atomic chains, crystals with dislocations, and superconducting nanowires, etc.
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Affiliation(s)
- Yuhui Luo
- Faculty of Civil Engineering and Mechanics/Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China.,College of Physics and Information Engineering, Zhaotong University, Zhaotong 657000, China
| | - Chunhua Zeng
- Faculty of Civil Engineering and Mechanics/Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
| | - Bao-Quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement, SPTE, South China Normal University, Guangzhou 510006, China
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