Correspondence behavior of classical and quantum dissipative directed transport via thermal noise

TL;DR

This paper investigates the classical-quantum correspondence in dissipative ratchet models, showing generally good agreement in asymptotic currents and eigenvalue spectra, with quantum coherences playing a key role.

Contribution

It systematically compares classical and quantum dissipative ratchet behaviors, revealing the conditions under which their dynamics and spectra align or diverge.

Findings

Classical and quantum asymptotic currents generally match well.

Eigenvalue spectra of classical and quantum operators are closely related.

Quantum coherences influence the asymptotic states significantly.

Abstract

We systematically study several classical-quantum correspondence properties of the dissipative modified kicked rotator, a paradigmatic ratchet model. We explore the behavior of the asymptotic currents for finite $\hbar_{\rm eff}$ values in a wide range of the parameter space. We find that the correspondence between the classical currents with thermal noise providing uctuations of size $\hbar_{\rm eff}$ and the quantum ones without it, is very good in general with the exception of specific regions. We systematically consider the spectra of the corresponding classical Perron-Frobenius operators and quantum superoperators. By means of an average distance between the classical and quantum sets of eigenvalues we find that the correspondence is unexpectedly quite uniform. This apparent contradiction is solved with the help of the Weyl-Wigner distributions of the equilibrium eigenvectors, which reveal the key role of quantum effects by showing surviving coherences in the asymptotic states.