Statistical Approach to Quantum Chaotic Ratchets

TL;DR

This paper introduces a statistical approach to quantum chaotic ratchets, predicting a Gaussian distribution of current over phase-space uniform initial states with numerical validation, revealing stronger effects than traditional states.

Contribution

It is the first to analyze the statistical properties of quantum ratchet currents over phase-space uniform initial states in chaotic systems.

Findings

Current distribution is Gaussian with zero mean and variance proportional to Dħ².

Variance of the current is larger than for momentum states.

Predicted effects are strong enough for experimental observation.

Abstract

The quantum ratchet effect in fully chaotic systems is approached by studying, for the first time, \emph{statistical} properties of the ratchet current over well-defined sets of initial states. Natural initial states in a semiclassical regime are those that are \emph{phase-space uniform} with the \emph{maximal possible} resolution of one Planck cell. General arguments in this regime, for quantum-resonance values of a scaled Planck constant $\hbar$, predict that the distribution of the current over all such states is a zero-mean Gaussian with variance $\sim D\hbar^{2}/(2\pi^{2})$, where $D$ is the chaotic-diffusion coefficient. This prediction is well supported by extensive numerical evidence. The average strength of the effect, measured by the variance above, is \emph{significantly larger} than that for the usual momentum states and other states. Such strong effects should be experimentally observable.