Quantum Parameter Space of Dissipative Directed Transport

TL;DR

This paper investigates the quantum parameter space of dissipative systems, revealing how classical structures influence quantum behavior and introducing the concept of parametric tunneling that blurs classical boundaries.

Contribution

It provides a detailed numerical analysis of quantum dissipative ratchets, confirming the classical shape of isoperiodic stable structures and introducing the parametric tunneling mechanism.

Findings

Classical ISS shapes are preserved in quantum systems.

Quantum parameter space exhibits blurred borders due to parametric tunneling.

Quantum states show reduced maximum directed currents.

Abstract

Quantum manifestations of isoperiodic stable structures (QISSs) have a crucial role in the current behavior of quantum dissipative ratchets. In this context, the simple shape of the ISSs has been conjectured to be an almost exclusive feature of the classical system. This has drastic consequences for many properties of the directed currents, the most important one being that it imposes a significant reduction in their maximum values, thus affecting the attainable efficiency at the quantum level. In this work we prove this conjecture by means of comprehensive numerical explorations and statistical analysis of the quantum states. We are able to describe the quantum parameter space of a paradigmatic system for different values of $\hbar_{\rm eff}$ in great detail. Moreover, thanks to this we provide evidence on a mechanism that we call parametric tunneling by which the sharp classical borders of the regions in parameter space become blurred in the quantum counterpart. We expect this to be a common property of generic dissipative quantum systems.