Classical to quantum correspondence in dissipative directed transport

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 modifiedkicked rotator. We study the spectral behavior of the corresponding classical Perron-Frobenius operators withthermal noise and the quantum superoperators without it for small eff values. We find a remarkable similaritybetween the classical and quantum spectra. This finding significantly extends previous results?obtained forthe mean currents and asymptotic distributions only?and, on the other hand, unveils a classical to quantumcorrespondence mechanism where the classical noise is qualitatively different from the quantum one. This iscrucial not only for simple attractors but also for chaotic ones, where just analyzing the asymptotic distribution isrevealed as insufficient. Moreover, we provide with a detailed characterization of relevant eigenvectors by meansof 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 isa universal feature of dissipative systems.