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G R A, Barik D. Roughness in the periodic potential induces absolute negative mobility in a driven Brownian ratchet. Phys Rev E 2022; 106:044129. [PMID: 36397596 DOI: 10.1103/physreve.106.044129] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2022] [Accepted: 10/03/2022] [Indexed: 06/16/2023]
Abstract
Absolute negative mobility, where particles move opposite to the direction as governed by the external load, is an anomalous transport property of a Brownian ratchet and has technological implications in mass separation and bioanalytical applications. We numerically investigated here the effect of roughness in symmetric periodic potential on the negative mobility of a driven inertial Brownian ratchet in the presence of an external load. We show that the microscopic spatial heterogeneity of the potential can generate negative mobility which would not otherwise be possible under smooth potential in the concerned parameter space. We determined the optimal condition in terms of parameter space for such anomalous behavior. Our calculations indicate that the shift of balance towards the negative velocity phase in the temporal oscillations of velocity and weakly chaotic dynamics are responsible factors for roughness-induced negative mobility. These calculations highlight a constructive role of roughness in the anomalous transport properties of Brownian ratchet.
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Affiliation(s)
- Archana G R
- School of Chemistry, University of Hyderabad, Gachibowli, 500046 Hyderabad, India
| | - Debashis Barik
- School of Chemistry, University of Hyderabad, Gachibowli, 500046 Hyderabad, India
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2
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Das M, Das D, Barik D, Ray DS. Landauer's blowtorch effect as a thermodynamic cross process: Brownian cooling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052102. [PMID: 26651642 DOI: 10.1103/physreve.92.052102] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2015] [Indexed: 06/05/2023]
Abstract
The local heating of a selected region in a double-well potential alters the relative stability of the two wells and gives rise to an enhancement of population transfer to the cold well. We show that this Landauer's blowtorch effect may be considered in the spirit of a thermodynamic cross process linearly connecting the flux of particles and the thermodynamic force associated with the temperature difference and consequently ensuring the existence of a reverse cross effect. This reverse effect is realized by directing the thermalized particles in a double-well potential by application of an external bias from one well to the other, which suffers cooling.
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Affiliation(s)
- Moupriya Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Debojyoti Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Debashis Barik
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Deb Shankar Ray
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
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3
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Spiechowicz J, Łuczka J. Josephson phase diffusion in the superconducting quantum interference device ratchet. CHAOS (WOODBURY, N.Y.) 2015; 25:053110. [PMID: 26026322 DOI: 10.1063/1.4921211] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We study diffusion of the Josephson phase in the asymmetric superconducting quantum interference device (SQUID) subjected to a time-periodic current and pierced by an external magnetic flux. We analyze a relation between phase diffusion and quality of transport characterized by the dc voltage across the SQUID and efficiency of the device. In doing so, we concentrate on the previously reported regime [J. Spiechowicz and J. Łuczka, New J. Phys. 17, 023054 (2015)] for which efficiency of the SQUID attains a global maximum. For long times, the mean-square displacement of the phase is a linear function of time, meaning that diffusion is normal. Its coefficient is small indicating rather regular phase evolution. However, it can be magnified several times by tailoring experimentally accessible parameters like amplitudes of the ac current or external magnetic flux. Finally, we prove that in the deterministic limit this regime is essentially non-chaotic and possesses an unexpected simplicity of attractors.
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Affiliation(s)
- Jakub Spiechowicz
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
| | - Jerzy Łuczka
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
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4
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Manchein C, Celestino A, Beims MW. Temperature resistant optimal ratchet transport. PHYSICAL REVIEW LETTERS 2013; 110:114102. [PMID: 25166540 DOI: 10.1103/physrevlett.110.114102] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2012] [Indexed: 06/03/2023]
Abstract
Stable periodic structures containing optimal ratchet transport, recently found in the parameter space dissipation versus ratchet parameter by [A. Celestino et al. Phys. Rev. Lett. 106, 234101 (2011)], are shown to be resistant to reasonable temperatures, reinforcing the expectation that they are essential to explain the optimal ratchet transport in nature. Critical temperatures for their destruction, valid from the overdamping to close to the conservative limits, are obtained numerically and shown to be connected to the current efficiency, given here analytically. A region where thermal activation of the rachet current takes place is also found, and its underlying mechanism is unveiled. Results are demonstrated for a discrete ratchet model and generalized to the Langevin equation with an additional external oscillating force.
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Affiliation(s)
- C Manchein
- Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil
| | - A Celestino
- Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, Brazil
| | - M W Beims
- Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, Brazil and Max-Planck-Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
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Zelan M, Hagman H, Labaigt G, Jonsell S, Dion CM. Experimental measurement of efficiency and transport coherence of a cold-atom Brownian motor in optical lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:020102. [PMID: 21405800 DOI: 10.1103/physreve.83.020102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2010] [Indexed: 05/30/2023]
Abstract
The rectification of noise into directed movement or useful energy is utilized by many different systems. The peculiar nature of the energy source and conceptual differences between such Brownian motor systems makes a characterization of the performance far from straightforward. In this work, where the Brownian motor consists of atoms interacting with dissipative optical lattices, we adopt existing theory and present experimental measurements for both the efficiency and the transport coherence. We achieve up to 0.3% for the efficiency and 0.01 for the Péclet number.
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Affiliation(s)
- M Zelan
- Department of Physics, Umeå University, SE-90187 Umeå, Sweden.
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Li JH, Łuczka J. Thermal-inertial ratchet effects: negative mobility, resonant activation, noise-enhanced stability, and noise-weakened stability. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:041104. [PMID: 21230235 DOI: 10.1103/physreve.82.041104] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2009] [Revised: 06/10/2010] [Indexed: 05/30/2023]
Abstract
Transport properties of a Brownian particle in thermal-inertial ratchets subject to an external time-oscillatory drive and a constant bias force are investigated. Since the phenomena of negative mobility, resonant activation and noise-enhance stability were reported before, in the present paper, we report some additional aspects of negative mobility, resonant activation and noise-enhance stability, such as the ingredients for the appearances of these phenomena, multiple resonant activation peaks, current reversals, noise-weakened stability, and so on.
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Affiliation(s)
- Jing-hui Li
- Faculty of Science, Ningbo University, Ningbo 315211, People's Republic of China
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7
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Kostur M, Luczka J, Hänggi P. Negative mobility induced by colored thermal fluctuations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:051121. [PMID: 20364961 DOI: 10.1103/physreve.80.051121] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2009] [Indexed: 05/29/2023]
Abstract
Anomalous transport of non-Markovian thermal Brownian particle dynamics in spatially periodic symmetric systems that is driven by time-periodic symmetric driving and constant bias is investigated numerically. The Brownian dynamics is modeled by a generalized Langevin equation with exponentially correlated Gaussian thermal noise, obeying the fluctuation-dissipation theorem. We study the role of nonzero correlation time of thermal fluctuations for the occurrence of absolute negative (linear) mobility (ANM) near zero bias, negative-valued, nonlinear mobility (NNM), and negative differential mobility (NDM) at finite bias away from equilibrium. We detect that a nonzero thermal correlation time can either enhance or also diminish the value of ANM. Moreover, finite thermal noise correlation can induce NDM and NNM in regions of parameter space for which such ANM and NNM behaviors are distinctly absent for limiting white thermal noise. In parts of the parameter space, we find a complex structure of regions of linear and nonlinear negative mobility: islands and tongues which emerge and vanish under parameters manipulation. While certain such anomalous transport regimes fade away with increasing temperature some specific regions interestingly remain rather robust. Outside those regimes with anomalous mobility, the ac/dc driven transport is either normal or the driven Brownian particles are not transported at all.
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Affiliation(s)
- M Kostur
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
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Saikia S, Mahato MC. Dispersionless motion and ratchet effect in a square-wave-driven inertial periodic potential system. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:175409. [PMID: 21825424 DOI: 10.1088/0953-8984/21/17/175409] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The underdamped Langevin equation of motion of a particle, in a symmetric periodic potential and subjected to a symmetric periodic forcing with mean zero over a period, with nonuniform friction, is solved numerically. The particle is shown to acquire a steady state mean velocity at asymptotically large timescales. At these large timescales the position dispersion grows proportionally with time, t, allowing for calculating the steady state diffusion coefficient D. Interestingly, D shows a peaking behaviour around the same F(0) where the net current peaks. The net (ratchet) current, however, turns out to be largely coherent. At an intermediate timescale, which bridges the small timescale behaviour of dispersion ∼t(2) to the large time one, the system shows periodic oscillation between dispersionless and steeply growing dispersion depending on the amplitude and frequency of the forcing. The contribution of these different dispersion regimes to ratchet current is analysed.
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Affiliation(s)
- S Saikia
- Department of Physics, North-Eastern Hill University, Shillong 793022, India. Department of Physics, St Anthony's College, Shillong 793001, India
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Machura L, Kostur M, Łuczka J. Transport characteristics of molecular motors. Biosystems 2008; 94:253-7. [PMID: 18721849 DOI: 10.1016/j.biosystems.2008.05.033] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2008] [Accepted: 05/26/2008] [Indexed: 10/21/2022]
Abstract
Properties of transport of molecular motors are investigated. A simplified model based on the concept of Brownian ratchets is applied. We analyze a stochastic equation of motion by means of numerical methods. The transport is systematically studied with respect to its energetic efficiency and quality expressed by an effective diffusion coefficient. We demonstrate the role of friction and non-equilibrium driving on the transport quantifiers and identify regions of a parameter space where motors are optimally transported.
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Affiliation(s)
- Lukasz Machura
- Institute of Physics, University of Silesia, Katowice, Poland.
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Son WS, Ryu JW, Hwang DU, Lee SY, Park YJ, Kim CM. Transport control in a deterministic ratchet system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:066213. [PMID: 18643356 DOI: 10.1103/physreve.77.066213] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2006] [Revised: 03/10/2008] [Indexed: 05/26/2023]
Abstract
We study the control of transport properties in a deterministic inertia ratchet system via the extended delay feedback method. A chaotic current of a deterministic inertia ratchet system is controlled to a regular current by stabilizing unstable periodic orbits embedded in a chaotic attractor of the unperturbed system. By selecting an unstable periodic orbit, which has a desired transport property, and stabilizing it via the extended delay feedback method, we can control transport properties of the deterministic inertia ratchet system. Also, we show that the extended delay feedback method can be utilized for separation of particles in the deterministic inertia ratchet system as a particle's initial condition varies.
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Affiliation(s)
- Woo-Sik Son
- National Creative Research Initiative Center for Quantum Chaos Applications, Sogang University, Seoul 121-742, Korea.
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11
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Ai BQ, Liu LG. Facilitated movement of inertial Brownian motors driven by a load under an asymmetric potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:042103. [PMID: 17995041 DOI: 10.1103/physreve.76.042103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2007] [Indexed: 05/25/2023]
Abstract
Based on recent work [L. Machura, M. Kostur, P. Talkner, J. Luczka, and P. Hanggi, Phys. Rev. Lett. 98, 040601 (2007)], we extend the study of inertial Brownian motors to the case of an asymmetric potential. It is found that some transport phenomena appear in the presence of an asymmetric potential. Within tailored parameter regimes, there exists two optimal values of the load at which the mean velocity takes its maximum, which means that a load can facilitate the transport in the two parameter regimes. In addition, the phenomenon of multiple current reversals can be observed when the load is increased.
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Affiliation(s)
- Bao-quan Ai
- Institute for Condensed Matter Physics, School of Physics and Telecommunication Engineering, and Laboratory of Photonic Information Technology, South China Normal University, 510006 Guangzhou, People's Republic of China.
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Kim C, Lee EK, Hänggi P, Talkner P. Numerical method for solving stochastic differential equations with Poissonian white shot noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:011109. [PMID: 17677412 DOI: 10.1103/physreve.76.011109] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2007] [Indexed: 05/16/2023]
Abstract
We propose a numerical integration scheme to solve stochastic differential equations driven by Poissonian white shot noise. Our formula, which is based on an integral equation, which is equivalent to the stochastic differential equation, utilizes a discrete time approximation with fixed integration time step. We show that our integration formula approaches the Euler formula if the Poissonian noise approaches the Gaussian white noise. The accuracy and efficiency of the proposed algorithm are examined by studying the dynamics of an overdamped particle driven by Poissonian white shot noise in a spatially periodic potential. We find that the accuracy of the proposed algorithm only weakly depends on the parameters characterizing the Poissonian white shot noise; this holds true even if the limit of Gaussian white noise is approached.
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Affiliation(s)
- Changho Kim
- Department of Chemistry and School of Molecular Science (BK21), Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea
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13
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Machura L, Kostur M, Talkner P, Łuczka J, Hänggi P. Absolute negative mobility induced by thermal equilibrium fluctuations. PHYSICAL REVIEW LETTERS 2007; 98:040601. [PMID: 17358750 DOI: 10.1103/physrevlett.98.040601] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2006] [Indexed: 05/14/2023]
Abstract
A novel transport phenomenon is identified that is induced by inertial Brownian particles which move in simple one-dimensional, symmetric periodic potentials under the influence of both a time periodic and a constant, biasing driving force. Within tailored parameter regimes, thermal equilibrium fluctuations induce the phenomenon of absolute negative mobility (ANM), which means that the particle noisily moves backwards against a small constant bias. When no thermal fluctuations act, the transport vanishes identically in these tailored regimes. ANM can also occur in the absence of fluctuations on grounds which are rooted solely in the complex, inertial deterministic dynamics. The experimental verification of this new transport scheme is elucidated for the archetype symmetric physical system: a convenient setup consisting of a resistively and capacitively shunted Josephson junction device.
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Affiliation(s)
- L Machura
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
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14
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Li JH. Chaotic noisy transport of electron pairs in a superconducting junction device: thermal-inertia ratchets. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:011114. [PMID: 16907067 DOI: 10.1103/physreve.74.011114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2005] [Indexed: 05/11/2023]
Abstract
Chaotic noisy transport of electron pairs in a superconducting junction device (thermal-inertia ratchets) is investigated. The study shows that when the temperature is low enough, the transport of the electron pairs can be mainly chaotic; when the temperature is high enough, it can be mainly stochastic. By controlling the temperature and the amplitude of the input ac signal, the current of electron pairs can be reversed.
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Affiliation(s)
- Jing-hui Li
- Faculty of Science, Ningbo University, Ningbo 315211, China
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Machura L, Kostur M, Talkner P, Luczka J, Hänggi P. Quantum diffusion in biased washboard potentials: strong friction limit. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:031105. [PMID: 16605498 DOI: 10.1103/physreve.73.031105] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2005] [Indexed: 05/08/2023]
Abstract
Diffusive transport properties of a quantum Brownian particle moving in a tilted spatially periodic potential and strongly interacting with a thermostat are explored. Apart from the average stationary velocity, we foremost investigate the diffusive behavior by evaluating the effective diffusion coefficient together with the corresponding Peclet number. Corrections due to quantum effects, such as quantum tunneling and quantum fluctuations, are shown to substantially enhance the effectiveness of diffusive transport if only the thermostat temperature resides within an appropriate interval of intermediate values.
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Affiliation(s)
- L Machura
- Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany
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