Emergence of continual directed flow in Hamiltonian systems

TL;DR

This paper introduces a minimal Hamiltonian model demonstrating how internal symmetry breaking and transient chaos lead to sustained directed flow, distinct from driven systems with intermittent transport.

Contribution

It presents a novel minimal Hamiltonian model showing how internal symmetry breaking and transient chaos produce continual directed flow.

Findings

Directed flow emerges from symmetry breaking and transient chaos.

Trajectories become regular and ballistic after transient chaos.

Transport differs from intermittent behavior in driven systems.

Abstract

We propose a minimal model for the emergence of a directed flow in autonomous Hamiltonian systems. It is shown that internal breaking of the spatio-temporal symmetries, via localised initial conditions, that are unbiased with respect to the transporting degree of freedom, and transient chaos conspire to form the physical mechanism for the occurrence of a current. Most importantly, after passage through the transient chaos, trajectories perform solely regular transporting motion so that the resulting current is of continual ballistic nature. This has to be distinguished from the features of transport reported previously for driven Hamiltonian systems with mixed phase space where transport is determined by intermittent behaviour exhibiting power-law decay statistics of the duration of regular ballistic periods.