Stationary Hamiltonian transport with dc bias

¹ Max-Planck Institut für Physik Komplexer Systeme - Nöthnitzer Str. 38 D-01187 Dresden, Germany
² Universität Augsburg, Institut für Physik - Universitätsstrasse 1 D-86135 Augsburg, Germany

Received: 16 December 2005
Accepted: 15 March 2006

Abstract

The dynamics of a particle in a symmetric periodic potential under the influence of a time-periodic field is characterized by a mixed phase space with regular and chaotic components. An additional external dc bias transforms the chaotic manifold into a domain with unbounded acceleration. We study the stationary transport which originates from the persisting invariant manifolds (regular islands, periodic orbits, and cantori) that are initially embedded in the chaotic manifold. We prove persistence and emergence of transporting islands. The transient dynamics of the accelerated 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 ideally suited for testing and observing our findings.