Directed transient long-range transport in a slowly driven Hamiltonian system of interacting particles

TL;DR

This paper investigates how a chain of coupled particles in a periodic potential exhibits directed long-range transport under a time-periodic drive, revealing transient dynamics and collective motion driven by invariant tori.

Contribution

It demonstrates the existence of directed collective motion and long-range transport in a many-particle Hamiltonian system driven by an external field, highlighting the role of invariant tori.

Findings

Transient long-range transport occurs with adiabatic slope-modulations.

Directed collective motion is observed in the driven many-particle system.

Transport direction depends on the initial phase of the external modulation.

Abstract

We study the Hamiltonian dynamics of a one-dimensional chain of linearly coupled particles in a spatially periodic potential which is subjected to a time-periodic mono-frequency external field. The average over time and space of the related force vanishes and hence, the system is effectively without bias which excludes any ratchet effect. We pay special attention to the escape of the entire chain when initially all of its units are distributed in a potential well. Moreover for an escaping chain we explore the possibility of the successive generation of a directed flow based on large accelerations. We find that for adiabatic slope-modulations due to the ac-field transient long-range transport dynamics arises whose direction is governed by the initial phase of the modulation. Most strikingly, that for the driven many particle Hamiltonian system directed collective motion is observed provides evidence for the existence of families of transporting invariant tori confining orbits in ballistic channels in the high dimensional phase spaces.