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

Abstract

We systematically study several classical-quantum correspondence properties of the dissipative modifiedkicked rotator, a paradigmatic ratchet model. We explore the behavior of the asymptotic currents for finite effvalues in a wide range of the parameter space. We find that the correspondence between the classical currentswith thermal noise providing fluctuations of size eff and the quantum ones without it is very good in generalwith the exception of specific regions. We systematically consider the spectra of the corresponding classicalPerron-Frobenius operators and quantum superoperators. By means of an average distance between the classicaland quantum sets of eigenvalues we find that the correspondence is unexpectedly quite uniform. This apparentcontradiction is solved with the help of the Weyl-Wigner distributions of the equilibrium eigenvectors, whichreveal the key role of quantum effects by showing surviving coherences in the asymptotic states.