Classical to quantum correspondence in dissipative directed transport

TL;DR

This paper investigates the spectral similarities between classical and quantum dissipative ratchet models, revealing a universal classical-quantum correspondence mechanism through spectral analysis and eigenvector characterization.

Contribution

It extends previous work by demonstrating a spectral similarity between classical and quantum systems, unveiling a classical-quantum correspondence mechanism in dissipative systems.

Findings

Classical and quantum spectra show remarkable similarity.

Classical noise differs qualitatively from quantum noise.

Eigenvector analysis reveals detailed classical-quantum similarities.

Abstract

We compare the quantum and classical properties of the (Quantum) Isoperiodic Stable Structures -- (Q)ISSs -- which organize the parameter space of a paradigmatic dissipative ratchet model, i.e. the dissipative modified kicked rotator. We study the spectral behavior of the corresponding classical Perron-Frobenius operators with thermal noise and the quantum superoperators without it for small $\hbar_{\rm eff}$ values. We find a remarkable similarity between the classical and quantum spectra. This finding significantly extends previous results -- obtained for the mean currents and asymptotic distributions only -- and on the other hand unveils a classical to quantum correspondence mechanism where the classical noise is qualitatively different from the quantum one. This is crucial not only for simple attractors but also for chaotic ones, where just analyzing the asymptotic distribution reveals insufficient. Moreover, we provide with a detailed characterization of relevant eigenvectors by means of the corresponding Weyl-Wigner distributions, in order to better identify similarities and differences. Finally, this model being generic, it allows us to conjecture that this classical to quantum correspondence mechanism is a universal feature of dissipative systems.