Directed transport in a classical lattice with a high-frequency driving

We analyze the dynamics of a classical particle in a spatially periodic potential under the influence of a periodic in time uniform force. It was shown by S. Flach and coworkers [Phys. Rev. Lett. 84, 2358 (2000)] that despite zero average force, directed transport is possible in the system. Asymptot...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2012-07, Vol.86 (1 Pt 2), p.016206-016206, Article 016206
Main Authors: Itin, A P, Neishtadt, A I
Format: Article
Language:English
Subjects:
Computer Simulation
Models, Theoretical
Motion
Stress, Mechanical
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Summary:We analyze the dynamics of a classical particle in a spatially periodic potential under the influence of a periodic in time uniform force. It was shown by S. Flach and coworkers [Phys. Rev. Lett. 84, 2358 (2000)] that despite zero average force, directed transport is possible in the system. Asymptotic description of this phenomenon for the case of slow driving was developed by X. Leoncini and coworkers [Phys. Rev. E 79, 026213 (2009)]. Here we consider the case of fast driving using the canonical perturbation theory. An asymptotic formula is derived for the average drift velocity as a function of the system parameters and the driving law. We show that directed transport arises in an effective Hamiltonian that does not possess chaotic dynamics, thereby clarifying the relation between chaos and transport in the system. Sufficient conditions for transport are derived.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.86.016206