Chaos and Correspondence in Classical and Quantum Hamiltonian Ratchets: A Heisenberg Approach

TL;DR

This paper explores how quantum ratchet effects can persist despite classical chaos, using a Heisenberg picture approach to reveal fundamental similarities and differences in classical and quantum dynamics.

Contribution

It introduces a Heisenberg-based perspective on ratchet dynamics, highlighting the persistence of quantum effects in chaotic regimes unlike classical systems.

Findings

Quantum ratchet effects can survive classical chaos.

Classical chaos suppresses ratchet effects, but quantum effects may not.

A unified perspective on classical and quantum ratchet mechanisms.

Abstract

Previous work [Gong and Brumer, Phys. Rev. Lett., 97, 240602 (2006)] motivates this study as to how asymmetry-driven quantum ratchet effects can persist despite a corresponding fully chaotic classical phase space. A simple perspective of ratchet dynamics, based on the Heisenberg picture, is introduced. We show that ratchet effects are in principle of common origin in classical and quantum mechanics, though full chaos suppresses these effects in the former but not necessarily the latter. The relationship between ratchet effects and coherent dynamical control is noted.