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Hashemi A, Gilman ET, Khair AS. A multiple-timing analysis of temporal ratcheting. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2024; 47:28. [PMID: 38676815 PMCID: PMC11055766 DOI: 10.1140/epje/s10189-024-00421-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2024] [Accepted: 04/04/2024] [Indexed: 04/29/2024]
Abstract
We develop a two-timing perturbation analysis to provide quantitative insights on the existence of temporal ratchets in an exemplary system of a particle moving in a tank of fluid in response to an external vibration of the tank. We consider two-mode vibrations with angular frequencies ω and α ω , where α is a rational number. If α is a ratio of odd and even integers (e.g.,2 1 , 3 2 , 4 3 ), the system yields a net response: here, a nonzero time-average particle velocity. Our first-order perturbation solution predicts the existence of temporal ratchets for α = 2 . Furthermore, we demonstrate, for a reduced model, that the temporal ratcheting effect for α = 3 2 and4 3 appears at the third-order perturbation solution. More importantly, we find closed-form formulas for the magnitude and direction of the induced net velocities for these α values. On a broader scale, our methodology offers a new mathematical approach to study the complicated nature of temporal ratchets in physical systems.
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Affiliation(s)
- Aref Hashemi
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA.
- Courant Institute, New York University, New York, NY, USA.
| | - Edward T Gilman
- Department of Mathematics, Rice University, Houston, TX, USA
| | - Aditya S Khair
- Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA
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2
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Hashemi A, Tahernia M, Hui TC, Ristenpart WD, Miller GH. Net motion induced by nonantiperiodic vibratory or electrophoretic excitations with zero time average. Phys Rev E 2022; 105:065001. [PMID: 35854501 DOI: 10.1103/physreve.105.065001] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Accepted: 05/26/2022] [Indexed: 06/15/2023]
Abstract
It is well established that application of an oscillatory excitation with zero time-average but temporal asymmetry can yield net drift. To date this temporal symmetry breaking and net drift has been explored primarily in the context of point particles, nonlinear optics, and quantum systems. Here, we present two new experimental systems where the impact of temporally asymmetric force excitations can be readily observed with mechanical motion of macroscopic objects: (1) solid centimeter-scale objects placed on a uniform flat surface made to vibrate laterally, and (2) charged colloidal particles in water placed between parallel electrodes with an applied oscillatory electric potential. In both cases, net motion is observed both experimentally and numerically with nonantiperiodic, two-mode, sinusoids where the frequency modes are the ratio of odd and even numbers (e.g., 2Hz and 3Hz). The observed direction of motion is always the same for the same applied waveform, and is readily reversed by changing the sign of the applied waveform, for example, by swapping which electrode is powered and grounded. We extend these results to other nonlinear mechanical systems, and we discuss the implications for facile control of object motion using tunable periodic driving forces.
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Affiliation(s)
- Aref Hashemi
- Courant Institute, New York University, New York, New York, USA
| | - Mehrdad Tahernia
- Department of Information Engineering, The Chinese University of Hong Kong, China
| | - Timothy C Hui
- Department of Chemical Engineering, University of California Davis, Davis, California, USA
| | - William D Ristenpart
- Department of Chemical Engineering, University of California Davis, Davis, California, USA
| | - Gregory H Miller
- Department of Chemical Engineering, University of California Davis, Davis, California, USA
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3
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Abbasi-Pérez D, Sang H, Pérez-García L, Floris A, Amabilino DB, Raval R, Recio JM, Kantorovich L. Controlling the preferential motion of chiral molecular walkers on a surface. Chem Sci 2019; 10:5864-5874. [PMID: 31360390 PMCID: PMC6582760 DOI: 10.1039/c9sc01135h] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2019] [Accepted: 05/08/2019] [Indexed: 12/13/2022] Open
Abstract
Molecular walkers standing on two or more "feet" on an anisotropic periodic potential of a crystal surface may perform a one-dimensional Brownian motion at the surface-vacuum interface along a particular direction in which their mobility is the largest. In thermal equilibrium the molecules move with equal probabilities both ways along this direction, as expected from the detailed balance principle, well-known in chemical reactivity and in the theory of molecular motors. For molecules that possess an asymmetric potential energy surface (PES), we propose a generic method based on the application of a time-periodic external stimulus that would enable the molecules to move preferentially in a single direction thereby acting as Brownian ratchets. To illustrate this method, we consider a prototypical synthetic chiral molecular walker, 1,3-bis(imidazol-1-ylmethyl)-5(1-phenylethyl)benzene, diffusing on the anisotropic Cu(110) surface along the Cu rows. As unveiled by our kinetic Monte Carlo simulations based on the rates calculated using ab initio density functional theory, this molecule moves to the nearest equivalent lattice site via the so-called inchworm mechanism in which it steps first with the rear foot and then with the front foot. As a result, the molecule diffuses via a two-step mechanism, and due to its inherent asymmetry, the corresponding PES is also spatially asymmetric. Taking advantage of this fact, we show how the external stimulus can be tuned to separate molecules of different chirality, orientation and conformation. The consequences of these findings for molecular machines and the separation of enantiomers are also discussed.
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Affiliation(s)
- David Abbasi-Pérez
- Department of Physics , King's College London , London , WC2R 2LS , UK . ;
| | - Hongqian Sang
- Department of Physics , King's College London , London , WC2R 2LS , UK . ;
- Institute for Interdisciplinary Research , Jianghan University , Wuhan 430056 , China
| | - Lluïsa Pérez-García
- School of Pharmacy , University of Nottingham , University Park , Nottingham , NG7 2RD , UK
| | - Andrea Floris
- School of Chemistry , University of Lincoln , Brayford Pool , Lincoln LN6 7TS , UK
| | - David B Amabilino
- School of Chemistry , GSK Carbon Neutral Lab. for Sustainable Chemistry , University of Nottingham , Triumph Road , NG7 2TU , UK
| | - Rasmita Raval
- Surface Science Research Centre , Department of Chemistry , University of Liverpool , Liverpool L69 3BX , UK
| | - J Manuel Recio
- MALTA-Consolider Team and Department of Analytical and Physical Chemistry , Universidad de Oviedo , Oviedo , 33006 , Spain
| | - Lev Kantorovich
- Department of Physics , King's College London , London , WC2R 2LS , UK . ;
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4
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Schwemmer C, Fringes S, Duerig U, Ryu YK, Knoll AW. Experimental Observation of Current Reversal in a Rocking Brownian Motor. PHYSICAL REVIEW LETTERS 2018; 121:104102. [PMID: 30240236 DOI: 10.1103/physrevlett.121.104102] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2018] [Revised: 07/13/2018] [Indexed: 05/11/2023]
Abstract
A reversal of the particle current in overdamped rocking Brownian motors was predicted more than 20 years ago; however, an experimental verification and a deeper insight into this noise-driven mechanism remained elusive. Here, we investigate the high-frequency behavior of a rocking Brownian motor for 60 nm gold spheres based on electrostatic interaction in a 3D-shaped nanofluidic slit and electro-osmotic forcing of the particles. We measure the particle probability density in situ with 10 nm spatial and 250 μs temporal resolution and compare it with theory. At a driving frequency of 250 Hz, we observe a current reversal that can be traced to the asymmetric and increasingly static probability density at high frequencies.
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Affiliation(s)
| | - Stefan Fringes
- IBM Research GmbH, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
- Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Urs Duerig
- IBM Research GmbH, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
- SwissLitho AG, Technoparkstrasse 1, 8005 Zürich, Switzerland
| | - Yu Kyoung Ryu
- IBM Research GmbH, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Armin W Knoll
- IBM Research GmbH, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
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5
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Paul S, Santhanam MS. Floquet states of a kicked particle in a singular potential: Exponential and power-law profiles. Phys Rev E 2018; 97:032217. [PMID: 29776057 DOI: 10.1103/physreve.97.032217] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2017] [Indexed: 11/06/2022]
Abstract
It is well known that, in the chaotic regime, all the Floquet states of kicked rotor system display an exponential profile resulting from dynamical localization. If the kicked rotor is placed in an additional stationary infinite potential well, its Floquet states display power-law profile. It has also been suggested in general that the Floquet states of periodically kicked systems with singularities in the potential would have power-law profile. In this work, we study the Floquet states of a kicked particle in finite potential barrier. By varying the height of finite potential barrier, the nature of transition in the Floquet state from exponential to power-law decay profile is studied. We map this system to a tight-binding model and show that the nature of decay profile depends on energy band spanned by the Floquet states (in unperturbed basis) relative to the potential height. This property can also be inferred from the statistics of Floquet eigenvalues and eigenvectors. This leads to an unusual scenario in which the level spacing distribution, as a window in to the spectral correlations, is not a unique characteristic for the entire system.
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Affiliation(s)
- Sanku Paul
- Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
| | - M S Santhanam
- Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
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6
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McDermott D, Olson Reichhardt CJ, Reichhardt C. Collective ratchet effects and reversals for active matter particles on quasi-one-dimensional asymmetric substrates. SOFT MATTER 2016; 12:8606-8615. [PMID: 27714306 DOI: 10.1039/c6sm01394e] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Using computer simulations, we study a two-dimensional system of sterically interacting self-mobile run-and-tumble disk-shaped particles with an underlying periodic quasi-one-dimensional asymmetric substrate, and show that a rich variety of collective active ratchet behaviors arise as a function of particle density, activity, substrate period, and the maximum force exerted by the substrate. The net dc drift, or ratchet transport flux, is nonmonotonic since it increases with increased activity but is diminished by the onset of self-clustering of the active particles. Increasing the particle density decreases the ratchet transport flux for shallow substrates but increases the ratchet transport flux for deep substrates due to collective hopping events. At the highest particle densities, the ratchet motion is destroyed by a self-jamming effect. We show that it is possible to realize reversals of the direction of the net dc drift in the deep substrate limit when multiple rows of active particles can be confined in each substrate minimum, permitting emergent particle-like excitations to appear that experience an inverted effective substrate potential. We map out a phase diagram of the forward and reverse ratchet effects as a function of the particle density, activity, and substrate properties.
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Affiliation(s)
- Danielle McDermott
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. and Department of Physics, Wabash College, Crawfordsville, Indiana 47933, USA
| | | | - Charles Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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7
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Ruyin C, Wanli P, Jianqiang Z, Linru N. Multiple absolute negative mobilities. CHAOS (WOODBURY, N.Y.) 2016; 26:093113. [PMID: 27781482 DOI: 10.1063/1.4961966] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In this paper, we investigate transport of an inertial particle in a spatially symmetric potential and subjected to two harmonic signals with different frequencies in both deterministic and stochastic cases. Numerical results indicate that: (i) In the deterministic case, the two harmonic signals can induce many (up to six) segments of negative slopes in the curve of mean velocity vs. external constant force, i.e., a multiple absolute negative mobilities (ANMs) effect. But the occurrence of the effect depends on their frequencies and amplitudes. (ii) For the stochastic case, the multiple ANMs relay on stable index and symmetry parameter of the Lévy noise. In the case of symmetric noise, appropriate stable index makes the multiple ANMs be the strongest. Our further investigations indicate that an indispensable condition for the multiple ANMs to occur in the system is the temporal symmetry breaking by one multiplicative periodic signal and one additive periodic signal.
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Affiliation(s)
- Chen Ruyin
- Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China
| | - Pan Wanli
- Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China
| | - Zhang Jianqiang
- Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China
| | - Nie Linru
- Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China
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8
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Grossert C, Leder M, Denisov S, Hänggi P, Weitz M. Experimental control of transport resonances in a coherent quantum rocking ratchet. Nat Commun 2016; 7:10440. [PMID: 26852803 PMCID: PMC4748114 DOI: 10.1038/ncomms10440] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2015] [Accepted: 12/10/2015] [Indexed: 01/04/2023] Open
Abstract
The ratchet phenomenon is a means to get directed transport without net forces. Originally conceived to rectify stochastic motion and describe operational principles of biological motors, the ratchet effect can be used to achieve controllable coherent quantum transport. This transport is an ingredient of several perspective quantum devices including atomic chips. Here we examine coherent transport of ultra-cold atoms in a rocking quantum ratchet. This is realized by loading a rubidium atomic Bose–Einstein condensate into a periodic optical potential subjected to a biharmonic temporal drive. The achieved long-time coherence allows us to resolve resonance enhancement of the atom transport induced by avoided crossings in the Floquet spectrum of the system. By tuning the strength of the temporal modulations, we observe a bifurcation of a single resonance into a doublet. Our measurements reveal the role of interactions among Floquet eigenstates for quantum ratchet transport. The ratchet effect can be used as a tool to control coherent quantum transport of ultra-cold atoms. Here, the authors demonstrate a rocking quantum ratchet with a rubidium BEC, and reveal the existence of quantum transport resonances.
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Affiliation(s)
- Christopher Grossert
- Institut für Angewandte Physik der Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
| | - Martin Leder
- Institut für Angewandte Physik der Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
| | - Sergey Denisov
- Department of Applied Mathematics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603950, Russia.,Institut für Physik, Universität Augsburg, Universitätsstr. 1, 86159 Augsburg, Germany.,Sumy State University, Rimsky-Korsakov Street 2, 40007 Sumy, Ukraine
| | - Peter Hänggi
- Department of Applied Mathematics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603950, Russia.,Institut für Physik, Universität Augsburg, Universitätsstr. 1, 86159 Augsburg, Germany.,Nanosystems Initiative Munich, Schellingstr. 4, D-80799 München, Germany
| | - Martin Weitz
- Institut für Angewandte Physik der Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
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9
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Sarkar P, Maity AK, Shit A, Chattopadhyay S, Chaudhuri JR, Banik SK. Controlling mobility via rapidly oscillating time-periodic stimulus. Chem Phys Lett 2014. [DOI: 10.1016/j.cplett.2014.03.062] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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10
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Casado-Pascual J, Cubero D, Renzoni F. Universal asymptotic behavior in nonlinear systems driven by a two-frequency forcing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062919. [PMID: 24483543 DOI: 10.1103/physreve.88.062919] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2013] [Indexed: 06/03/2023]
Abstract
We examine the time-dependent behavior of a nonlinear system driven by a two-frequency forcing. By using a nonperturbative approach, we are able to derive an asymptotic expression, valid in the long-time limit, for the time average of the output variable which describes the response of the system. We identify several universal features of the asymptotic response of the system, which are independent of the details of the model. In particular, we determine an asymptotic expression for the width of the resonance observed by keeping one frequency fixed and varying the other one. We show that this width is smaller than the usually assumed Fourier width by a factor determined by the two driving frequencies, and independent of the model system parameters. Additional general features can also be identified depending on the specific symmetry properties of the system. Our results find direct application in the study of sub-Fourier signal processing with nonlinear systems.
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Affiliation(s)
- Jesús Casado-Pascual
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, 41080 Sevilla, Spain
| | - David Cubero
- Departamento de Física Aplicada I, EUP, Universidad de Sevilla, Calle Virgen de África 7, 41011 Sevilla, Spain
| | - Ferruccio Renzoni
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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11
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Machura L, Spiechowicz J, Kostur M, Łuczka J. Two coupled Josephson junctions: dc voltage controlled by biharmonic current. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:085702. [PMID: 22277582 DOI: 10.1088/0953-8984/24/8/085702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We study transport properties of two Josephson junctions coupled by an external shunt resistance. One of the junctions (say, the first) is driven by an unbiased ac current consisting of two harmonics. The device can rectify the ac current yielding a dc voltage across the first junction. For some values of coupling strength, controlled by an external shunt resistance, a dc voltage across the second junction can be generated. By variation of system parameters such as the relative phase or frequency of two harmonics, one can conveniently manipulate both voltages with high efficiency, e.g. changing the dc voltages across the first and second junctions from positive to negative values and vice versa.
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Affiliation(s)
- L Machura
- Institute of Physics, University of Silesia, Katowice, Poland
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12
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Maragó OM, Bonaccorso F, Saija R, Privitera G, Gucciardi PG, Iatì MA, Calogero G, Jones PH, Borghese F, Denti P, Nicolosi V, Ferrari AC. Brownian motion of graphene. ACS NANO 2010; 4:7515-7523. [PMID: 21133432 DOI: 10.1021/nn1018126] [Citation(s) in RCA: 82] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Brownian motion is a manifestation of the fluctuation-dissipation theorem of statistical mechanics. It regulates systems in physics, biology, chemistry, and finance. We use graphene as prototype material to unravel the consequences of the fluctuation-dissipation theorem in two dimensions, by studying the Brownian motion of optically trapped graphene flakes. These orient orthogonal to the light polarization, due to the optical constants anisotropy. We explain the flake dynamics in the optical trap and measure force and torque constants from the correlation functions of the tracking signals, as well as comparing experiments with a full electromagnetic theory of optical trapping. The understanding of optical trapping of two-dimensional nanostructures gained through our Brownian motion analysis paves the way to light-controlled manipulation and all-optical sorting of biological membranes and anisotropic macromolecules.
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Affiliation(s)
- Onofrio M Maragó
- CNR-Istituto per i Processi Chimico-Fisici, I-98158 Messina, Italy.
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13
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Tierno P, Reimann P, Johansen TH, Sagués F. Giant transversal particle diffusion in a longitudinal magnetic ratchet. PHYSICAL REVIEW LETTERS 2010; 105:230602. [PMID: 21231443 DOI: 10.1103/physrevlett.105.230602] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2010] [Indexed: 05/30/2023]
Abstract
We study the transversal motion of paramagnetic particles on a uniaxial garnet film, exhibiting a longitudinal ratchet effect in the presence of an oscillating magnetic field. Without the field, the thermal diffusion coefficient obtained by video microscopy is D(0) ≈ 3 × 10(-4) μm2/s. With the field, the transversal diffusion exhibits a giant enhancement by almost four decades and a pronounced maximum as a function of the driving frequency. We explain the experimental findings with a theoretical interpretation in terms of random disorder effects within the magnetic film.
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Affiliation(s)
- Pietro Tierno
- Departament de Química Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain.
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14
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Żabicki M, Ebeling W, Gudowska-Nowak E. The thermodynamic cycle of an entropy-driven stepper motor walking hand-over-hand. Chem Phys 2010. [DOI: 10.1016/j.chemphys.2010.06.003] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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15
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Cubero D, Lebedev V, Renzoni F. Current reversals in a rocking ratchet: dynamical versus symmetry-breaking mechanisms. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:041116. [PMID: 21230247 DOI: 10.1103/physreve.82.041116] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2010] [Indexed: 05/30/2023]
Abstract
Directed transport in ratchets is determined by symmetry breaking in a system out of equilibrium. A hallmark of rocking ratchets is current reversals: an increase in the rocking force changes the direction of the current. In this work for a biharmonically driven spatially symmetric rocking ratchet we show that a class of current reversal is precisely determined by symmetry breaking, thus creating a link between dynamical and symmetry-breaking mechanisms.
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Affiliation(s)
- D Cubero
- Departamento de Física Aplicada I, EUP, Universidad de Sevilla, Calle Virgen de África 7, 41011 Sevilla, Spain
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16
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He Y, Ai BQ. Enhancement of the longitudinal transport by a weakly transversal drive. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:021110. [PMID: 20365533 DOI: 10.1103/physreve.81.021110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2009] [Indexed: 05/29/2023]
Abstract
Transport of Brownian particles in a two-dimensional asymmetric tube is investigated by applying a polarized field. From the Brownian dynamics simulations, we find that the longitudinal current can be enhanced remarkably by applying a weakly transversal drive. Multiple current reversals can be realized by altering the driving frequency of the polarized field. By coupling the longitudinal and transversal forces together, one can control the particle transport flexibly.
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Affiliation(s)
- Yafeng He
- Laboratory of Quantum Information Technology, ICMP and SPTE, South China Normal University, 510006 Guangzhou, China and College of Physics Science and Technology, Hebei University, 071002 Baoding, China.
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17
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Sterck A, Koelle D, Kleiner R. Rectification in a stochastically driven three-junction SQUID rocking ratchet. PHYSICAL REVIEW LETTERS 2009; 103:047001. [PMID: 19659390 DOI: 10.1103/physrevlett.103.047001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2009] [Indexed: 05/28/2023]
Abstract
A three-junction SQUID forms a rocking ratchet for the phase differences across the Josephson junctions. In this Letter we investigate its capability to rectify voltages under stochastic drive currents with a white frequency spectrum up to a cutoff frequency f_{cut}. Experimentally, we accessed the adiabatic regime and find very good agreement with theory. Numerically, we also investigated large values of f_{cut} and find, in agreement with the laws of thermodynamics, that the response disappears, as f_{cut} becomes much larger than the characteristic frequency scales of the system.
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Affiliation(s)
- A Sterck
- Physikalisches Institut and Center for Collective Quantum Phenomena, Universität Tübingen, D-72076 Tübingen, Germany
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18
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Ponomarev AV, Denisov S, Hänggi P. ac-driven atomic quantum motor. PHYSICAL REVIEW LETTERS 2009; 102:230601. [PMID: 19658915 DOI: 10.1103/physrevlett.102.230601] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2009] [Revised: 04/10/2009] [Indexed: 05/28/2023]
Abstract
We propose an ac-driven quantum motor consisting of two different, interacting ultracold atoms placed into a ring-shaped optical lattice and submerged in a pulsating magnetic field. While the first atom carries a current, the second one serves as a quantum starter. For fixed zero-momentum initial conditions the asymptotic carrier velocity converges to a unique nonzero value. We also demonstrate that this quantum motor performs work against a constant load.
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Affiliation(s)
- A V Ponomarev
- Institute of Physics, University of Augsburg, Universitätstrasse 1, D-86159 Augsburg, Germany
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19
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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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20
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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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Gommers R, Lebedev V, Brown M, Renzoni F. Gating ratchet for cold atoms. PHYSICAL REVIEW LETTERS 2008; 100:040603. [PMID: 18352250 DOI: 10.1103/physrevlett.100.040603] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2007] [Revised: 10/30/2007] [Indexed: 05/26/2023]
Abstract
We demonstrate experimentally a gating ratchet with cold rubidium atoms in a driven near-resonant optical lattice. A single-harmonic periodic modulation of the optical potential depth is applied, together with a single-harmonic rocking force. Directed motion is observed as a result of the breaking of the symmetries of the system.
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Affiliation(s)
- R Gommers
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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22
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Chaudhuri JR, Chattopadhyay S, Banik SK. Simple model for transport phenomena: Microscopic construction of Maxwell demonlike engine. J Chem Phys 2007; 127:224508. [DOI: 10.1063/1.2806301] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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23
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Jones PH, Goonasekera M, Meacher DR, Jonckheere T, Monteiro TS. Directed motion for delta-kicked atoms with broken symmetries: comparison between theory and experiment. PHYSICAL REVIEW LETTERS 2007; 98:073002. [PMID: 17359021 DOI: 10.1103/physrevlett.98.073002] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2006] [Indexed: 05/14/2023]
Abstract
We report an experimental investigation of momentum diffusion in the delta-function kicked rotor where time symmetry is broken by a two-period kicking cycle and spatial symmetry by an alternating linear potential. We exploit this, and a technique involving a moving optical potential, to create an asymmetry in the momentum diffusion that is due to the classical chaotic diffusion. This represents a realization of a type of Hamiltonian quantum ratchet.
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Affiliation(s)
- P H Jones
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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24
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Sjölund P, Petra SJH, Dion CM, Jonsell S, Nylén M, Sanchez-Palencia L, Kastberg A. Demonstration of a controllable three-dimensional Brownian motor in symmetric potentials. PHYSICAL REVIEW LETTERS 2006; 96:190602. [PMID: 16803094 DOI: 10.1103/physrevlett.96.190602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2005] [Indexed: 05/10/2023]
Abstract
We demonstrate a Brownian motor, based on cold atoms in optical lattices, where isotropic random fluctuations are rectified in order to induce controlled atomic motion in arbitrary directions. In contrast to earlier demonstrations of ratchet effects, our Brownian motor operates in potentials that are spatially and temporally symmetric, but where spatiotemporal symmetry is broken by a phase shift between the potentials and asymmetric transfer rates between them. The Brownian motor is demonstrated in three dimensions and the noise-induced drift is controllable in our system.
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Affiliation(s)
- P Sjölund
- Department of Physics, Umeå University, Sweden
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25
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Douglas P, Bergamini S, Renzoni F. Tunable Tsallis distributions in dissipative optical lattices. PHYSICAL REVIEW LETTERS 2006; 96:110601. [PMID: 16605807 DOI: 10.1103/physrevlett.96.110601] [Citation(s) in RCA: 75] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2006] [Indexed: 05/08/2023]
Abstract
We demonstrated experimentally that the momentum distribution of cold atoms in dissipative optical lattices is a Tsallis distribution. The parameters of the distribution can be continuously varied by changing the parameters of the optical potential. In particular, by changing the depth of the optical lattice, it is possible to change the momentum distribution from Gaussian, at deep potentials, to a power-law tail distribution at shallow optical potentials.
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Affiliation(s)
- P Douglas
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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Machura L, Kostur M, Marchesoni F, Talkner P, Hänggi P, Luczka J. Optimal strategy for controlling transport in inertial Brownian motors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2005; 17:S3741-S3752. [PMID: 21690721 DOI: 10.1088/0953-8984/17/47/007] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
In order to optimize the directed motion of an inertial Brownian motor, we identify the operating conditions that both maximize the motor current and minimize its dispersion. Extensive numerical simulation of an inertial rocked ratchet displays that two quantifiers, namely the energetic efficiency and the Péclet number (or equivalently the Fano factor), suffice to determine the regimes of optimal transport. The effective diffusion of this rocked inertial Brownian motor can be expressed as a generalized fluctuation theorem of the Green-Kubo type.
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Affiliation(s)
- Lukasz Machura
- Institute of Physics, University of Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany. Institute of Physics, University of Silesia, P-40-007 Katowice, Poland
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27
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Gommers R, Bergamini S, Renzoni F. Dissipation-induced symmetry breaking in a driven optical lattice. PHYSICAL REVIEW LETTERS 2005; 95:073003. [PMID: 16196778 DOI: 10.1103/physrevlett.95.073003] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2005] [Indexed: 05/04/2023]
Abstract
We analyze the atomic dynamics in an ac driven periodic optical potential which is symmetric in both time and space. We experimentally demonstrate that in the presence of dissipation the symmetry is broken, and a current of atoms through the optical lattice is generated as a result.
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Affiliation(s)
- R Gommers
- Department of Physics and Astronomy, University College London, UK
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Lee SH, Grier DG. Flux reversal in a two-state symmetric optical thermal ratchet. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:060102. [PMID: 16089710 DOI: 10.1103/physreve.71.060102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2005] [Revised: 04/04/2005] [Indexed: 05/03/2023]
Abstract
A Brownian particle's random motions can be rectified by a periodic potential-energy landscape that alternates between two states, even if both states are spatially symmetric. If the two states differ only by a discrete translation, the direction of the ratchet-driven current can be reversed by changing their relative durations. We experimentally demonstrate flux reversal in a symmetric two-state ratchet by tracking the motions of colloidal spheres moving through large arrays of discrete potential-energy wells created with dynamic holographic optical tweezers. The model's simplicity and high degree of symmetry suggest possible applications in molecular-scale motors.
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Affiliation(s)
- Sang-Hyuk Lee
- Department of Physics and Center for Soft Matter Research, New York University, New York, New York 10003, USA
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Gommers R, Douglas P, Bergamini S, Goonasekera M, Jones PH, Renzoni F. Resonant activation in a nonadiabatically driven optical lattice. PHYSICAL REVIEW LETTERS 2005; 94:143001. [PMID: 15904060 DOI: 10.1103/physrevlett.94.143001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2004] [Indexed: 05/02/2023]
Abstract
We demonstrate the phenomenon of resonant activation in a nonadiabatically driven dissipative optical lattice with broken time symmetry. The resonant activation results in a resonance as a function of the driving frequency in the current of atoms through the periodic potential. We demonstrate that the resonance is produced by the interplay between deterministic driving and fluctuations, and we also show that by changing the frequency of the driving it is possible to control the direction of the diffusion.
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Affiliation(s)
- R Gommers
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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Lee SH, Ladavac K, Polin M, Grier DG. Observation of flux reversal in a symmetric optical thermal ratchet. PHYSICAL REVIEW LETTERS 2005; 94:110601. [PMID: 15903837 DOI: 10.1103/physrevlett.94.110601] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2004] [Indexed: 05/02/2023]
Abstract
We demonstrate that a cycle of three holographic optical trapping patterns can implement a thermal ratchet for diffusing colloidal spheres and that the ratchet-driven transport displays flux reversal as a function of the cycle frequency and the intertrap separation. Unlike previously described ratchet models, the approach we describe involves three equivalent states, each of which is locally and globally spatially symmetric, with spatiotemporal symmetry being broken by the sequence of states.
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Affiliation(s)
- Sang-Hyuk Lee
- Department of Physics and Center for Soft Matter Research, New York University, New York, NY 10003, USA
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