dc-biased stationary transport in the absence of dissipation

TL;DR

This paper demonstrates how a Hamiltonian system with ac driving and a dc bias can sustain stationary transport, revealing the role of invariant manifolds and mixed phase space structures, with potential experimental realization using cold atoms.

Contribution

It introduces a novel mechanism for stationary current in Hamiltonian systems with ac and dc fields, emphasizing the role of invariant manifolds in transport without dissipation.

Findings

Existence of stationary current due to invariant manifolds

Separation of chaotic and regular dynamics by dc bias

Potential observation in cold atom experiments

Abstract

We obtain stationary transport in a Hamiltonian system with ac driving in the presence of a dc bias. A particle in a periodic potential under the influence of a time-periodic field possesses a mixed phase space with regular and chaotic components. An additional external dc bias allows to separate effectively these structures. We show the existence of a stationary current which originates from the persisting invariant manifolds (regular islands, periodic orbits, and cantori). The transient dynamics of the accelerated chaotic domain separates fast chaotic motion from ballistic type trajectories which stick to the vicinity of the invariant submanifold. Experimental studies with cold atoms in laser-induced optical lattices are ideal candidates for the observation of these unexpected findings.