Dynamical mechanisms of dc current generation in driven Hamiltonian systems

Денисов, С. В.; Flach, Sergej

doi:10.1103/physreve.64.056236

Cited by 61 publications

(85 citation statements)

References 12 publications

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“…The appearance of a nonzero dc-current J ch = lim t→∞ 1/t t t0 p(t ′ )dt ′ in this case is due to a desymmetrization of the chaotic layer structure (Fig.1a). It induces a desymmetrization of the events of directed motion to the right and left [28]. Due to ergodicity inside the layer, the asymptotic current is independent of the initial time t 0 , for initial conditions located inside the chaotic layer.…”

Section: Relevant Symmetries and Their Violations A Classical Lmentioning

confidence: 99%

Periodically driven quantum ratchets: Symmetries and resonances

et al. 2007

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We study the quantum version of a tilting and flashing Hamiltonian ratchets, consisting of a periodic potential and a time-periodic driving field. The system dynamics is governed by a Floquet evolution matrix bearing the symmetry of the corresponding Hamiltonian. The dc-current appears due to the desymmetrization of Floquet eigenstates, which become transporting when all the relevant symmetries are violated. Those eigenstates which mostly contribute to a directed transport reside in phase space regions corresponding to classical resonances. Quantum dynamics leads to the dependence of the average velocity on the initial phase of the ac-field. A resonant enhancement (or suppression) of the dc-current, due to avoided crossings between different Floquet states takes place upon tuning some control parameters. Our studies are predominantly aimed at experimental realizations of ac-driven quantum ratchets with cold atoms.

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Section: Relevant Symmetries and Their Violations A Classical Lmentioning

confidence: 99%

Periodically driven quantum ratchets: Symmetries and resonances

et al. 2007

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“…As in Refs. [4,5], this decomposition can, e.g., consist of a few prominent ballistic channels and some remaining chaotic "bulk" region. Our main point is here that in general it is not possible to approximate this remainder by an undirected and purely diffusive dynamics, i.e., to set v j = 0 for the corresponding subset in Eq.…”

Section: E Chaotic Transport and Lévy Walksmentioning

confidence: 99%

“…II E) is that the ballistic chaotic transport has nothing to do with internal structures of a chaotic phase-space component such as cantori or other partial transport barriers. All these complicated substructures, leading, e.g., to Lévy walks and anomalous diffusion in Hamiltonian ratchets [1,4,5], need not be considered in detail in order to understand that ballistic transport dominates for long times.…”

Section: Introductionmentioning

confidence: 99%

Directed chaotic transport in Hamiltonian ratchets

2005

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We present a comprehensive account of directed transport in one-dimensional Hamiltonian systems with spatial and temporal periodicity. They can be considered as Hamiltonian ratchets in the sense that ensembles of particles can show directed ballistic transport in the absence of an average force. We discuss general conditions for such directed transport, like a mixed classical phase space, and elucidate a sum rule that relates the contributions of different phase-space components to transport with each other. We show that regular ratchet transport can be directed against an external potential gradient while chaotic ballistic transport is restricted to unbiased systems. For quantized Hamiltonian ratchets we study transport in terms of the evolution of wave packets and derive a semiclassical expression for the distribution of level velocities which encode the quantum transport in the Floquet band spectra. We discuss the role of dynamical tunneling between transporting islands and the chaotic sea and the breakdown of transport in quantum ratchets with broken spatial periodicity.

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“…Trivial examples of this process are provided by integrable regular dynamics subjected to unbiased ac drives with fixed initial phase, i.e., not averaged over Goychuk and Hänggi, 2001͒. Much more intriguing are timedependent driven Hamiltonian quantum Brownian motors exhibiting a nontrivial, mixed classical phase space structure Denisov and Flach, 2001;Schanz et al, 2001. In these systems, the onset of a directed flow requires, apart from the necessity of breaking time-reversal symmetry, an additional dynamical symmetry breaking.…”

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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Dynamical mechanisms of dc current generation in driven Hamiltonian systems

Cited by 61 publications

References 12 publications

Periodically driven quantum ratchets: Symmetries and resonances

Periodically driven quantum ratchets: Symmetries and resonances

Directed chaotic transport in Hamiltonian ratchets

Artificial Brownian motors: Controlling transport on the nanoscale

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