title: 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 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 ℏ(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 is revealed as 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.
authors.affiliation: Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina.
authors.forename: Gabriel G
authors.initials: GG
authors.lastname: Carlo
authors.affiliation: Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina.
authors.forename: Alejandro M F
authors.initials: AM
authors.lastname: Rivas
authors.affiliation: Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina.
authors.forename: María E
authors.initials: ME
authors.lastname: Spina