Directed chaotic transport in Hamiltonian ratchets

Schanz, Holger; Dittrich, Thomas; Ketzmerick, Roland

doi:10.1103/physreve.71.026228

Cited by 103 publications

(145 citation statements)

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“…The concept of Hamiltonian quantum Brownian motors extends as well to fully quantum systems governed by a unitary time evolution ͑Goychuk and Schanz et al, 2001Schanz et al, , 2005Denisov et al, 2006Denisov et al, , 2007Gong et al, 2007͒. In fact, the issue of pure quantum coherence in the directed transport of chaotic Hamiltonian systems is presently a topic of active research.…”

Section: Hamiltonian Quantum Ratchet For Cold Atomsmentioning

confidence: 99%

Artificial Brownian motors: Controlling transport on the nanoscale

2009

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In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with unbiased external input signals, deterministic and random alike, can assist directed motion of particles at submicron scales. In such cases, one speaks of "Brownian motors." In this review the constructive role of Brownian motion is exemplified for various physical and technological setups, which are inspired by the cellular molecular machinery: the working principles and characteristics of stylized devices are discussed to show how fluctuations, either thermal or extrinsic, can be used to control diffusive particle transport. Recent experimental demonstrations of this concept are surveyed with particular attention to transport in artificial, i.e., nonbiological, nanopores, lithographic tracks, and optical traps, where single-particle currents were first measured. Much emphasis is given to two-and three-dimensional devices containing many interacting particles of one or more species; for this class of artificial motors, noise rectification results also from the interplay of particle Brownian motion and geometric constraints. Recently, selective control and optimization of the transport of interacting colloidal particles and magnetic vortices have been successfully achieved, thus leading to the new generation of microfluidic and superconducting devices presented here. The field has recently been enriched with impressive experimental achievements in building artificial Brownian motor devices that even operate within the quantum domain by harvesting quantum Brownian motion. Sundry akin topics include activities aimed at noise-assisted shuttling other degrees of freedom such as charge, spin, or even heat and the assembly of chemical synthetic molecular motors. This review ends with a perspective for future pathways and potential new applications.

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Section: Hamiltonian Quantum Ratchet For Cold Atomsmentioning

confidence: 99%

Artificial Brownian motors: Controlling transport on the nanoscale

2009

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“…This question has been subject of comprehensive research in the case of uniform driving (see e.g. [9,10,15,16]), and we are going to sum up the most important results. However, our main interest is on the impact of the partially broken shift symmetry induced by the spatiotemporal driving.…”

Section: The Floquet Spectrummentioning

confidence: 99%

“…One of the perks of using Floquet theory in order to study the dynamics of a time-dependent system is that once the FBMs are known, the asymptotic current can be calculated very conveniently as [9,10]:…”

Section: A Asymptotic Currentsmentioning

confidence: 99%

“…Hence, the stroboscopic time evolution of an arbitrary initial state can be calculated as [9] Ψ(x, mT…”

Section: A Floquet-bloch Theorymentioning

confidence: 99%

“…While some of these experiments are carried out at moderate temperatures and allow for a classical treatment [2][3][4], others could reach ultracold temperatures and demonstrated the accessibility of Hamiltonian ratchet setups operating deep in the quantum regime [5,6]. The experimental advancements concerning these newly realized 'quantum ratchets' were accompanied by a substantial body of theoretical works (see [7][8][9][10][11][12][13][14] and references therein). Thereby, one of the main achievements was the classification of the symmetries which need to be broken in order to allow for the observation of a ratchet current [15].…”

Section: Introductionmentioning

confidence: 99%

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Symmetries and transport in site-dependent driven quantum lattices

et al. 2014

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We explore the quantum dynamics of particles in a spatiotemporally driven lattice. A powerful numerical scheme is developed, which provides us with the Floquet modes and thus enables a stroboscopic propagation of arbitrary initial states. A detailed symmetry analysis represents the cornerstone for an intricate manipulation of the Floquet spectrum. Specifically, we show how exact crossings can be converted into avoided ones, while the width of these resulting avoided crossings can be engineered by adjusting parameters of the local driving. Asymptotic currents are shown to be controllable over a certain parameter range.

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Transporting Cold Atoms in Optical Lattices with Ratchets: Mechanisms and Symmetries

Денисов

Flach

Hänggi

2009

Springer Series in Optical Sciences

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Thermal fluctuations alone cannot create a steady directed transport in an unbiased system. However, if a system is out of equilibrium, the Second Law of Thermodynamics no longer applies, and then there are no thermodynamical constraints on the appearance of a steady transport [1,2]. A directed current can be generated out of a fluctuating (time-dependent) external field with zero mean. The corresponding ratchet effect [3,4,5,6,7,8] has been proposed as a physical mechanism of a microbiological motility more then a decade ago [4,5]. Later on the ratchet idea has found diverse applications in different areas [6,7,8], from a mechanical engine [9] up to quantum systems and quantum devices [10,11,12,13,14,15].When the deviation from an equilibrium regime is small (the case of weak external fields) one may use the linear response theory in order to estimate the answer of the system [16,17]. However, due to the linearization of the response, the current value will be strictly zero since the driving field has zero bias. Therefore, one has to take into account nonlinear corrections and then derive the corresponding nonlinear response functional [17,18], which may become a very complicated task, if the nonadiabatic regime is to be considered.To obtain a dc-current, one has to break certain discrete symmetries, which involve simultaneous transformations in space and time. A recently elaborated symmetry approach [19,20] established a clear relationship between the appearance of a directed current and broken space-time symmetries of the equations of motion. Thus, the symmetry analysis provides an information about the conditions for a directed transport appearance without the necessity of considering a nonlinear response functional.Most theoretical and experimental studies have focused on ratchet realizations at a noisy overdamped limit [6,7,8]. However, systematic studies of

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Directed chaotic transport in Hamiltonian ratchets

Cited by 103 publications

References 58 publications

Artificial Brownian motors: Controlling transport on the nanoscale

Artificial Brownian motors: Controlling transport on the nanoscale

Symmetries and transport in site-dependent driven quantum lattices

Transporting Cold Atoms in Optical Lattices with Ratchets: Mechanisms and Symmetries

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