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

TL;DR

This paper investigates how a classical particle in a periodic potential can exhibit directed transport under high-frequency driving, using perturbation theory to derive formulas and clarify the role of chaos.

Contribution

It develops an asymptotic formula for average drift velocity in high-frequency regimes and clarifies the connection between chaos and directed transport.

Findings

Directed transport occurs in an effective Hamiltonian without chaos.

An asymptotic formula for drift velocity is derived.

Conditions for the occurrence of transport are established.

Abstract

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 in [S.Flach, O.Yevtushenko, Y. Zolotaryuk, 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 in [X. Leoncini, A. Neishtadt, A. Vasiliev, Phys. Rev. E 79, 026213 (2009)]. Here we consider the case of fast driving using 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.