Quantum Isoperiodic Stable Structures and Directed Transport

TL;DR

This paper investigates quantum isoperiodic stable structures (QISSs) in dissipative ratchets, showing their relation to classical ISSs and chaotic attractors, and proposes a method to approximate QISSs using classical data plus thermal fluctuations.

Contribution

It introduces the concept of quantum ISSs, analyzes their properties, and suggests a novel approximation method using classical ISSs and thermal noise.

Findings

QISSs often resemble quantum chaotic attractors near classical ISSs.

Adding thermal fluctuations to classical ISSs approximates QISSs effectively.

Quantum chaotic attractors can be modeled using classical ISSs plus thermal noise.

Abstract

It has been recently found that the so called isoperiodic stable structures (ISSs) have a fundamental role in the classical current behavior of dissipative ratchets [Phys. Rev. Lett. {\bf 106}, 234101 (2011)]. Here I analyze their quantum counterparts, the quantum ISSs (QISSs), which have a fundamental role in the quantum current behavior. QISSs have the simple attractor shape of those ISSs which settle down in short times. However, in the majority of the cases they are strongly different from the ISSs, looking approximately the same as the quantum chaotic attractors that are at their vicinity in parameter space. By adding thermal fluctuations of the size of $\hbar_{\rm eff}$ to the ISSs I am able to obtain very good approximations to the QISSs. I conjecture that in general, quantum chaotic attractors could be well approximated by means of just the classical information of a neighboring ISS plus thermal fluctuations. I expect to find this behavior in quantum dissipative systems in general.