Classical limit of transport in quantum kicked maps

TL;DR

This paper explores how quantum effects like weak localization and shot noise diminish with increasing Ehrenfest time in chaotic quantum systems, confirming some theoretical predictions while revealing unexpected behavior in conductance fluctuations.

Contribution

It introduces a new method to compare semiclassical theory with numerical simulations based on the Ehrenfest time dependence of quantum effects.

Findings

Weak localization and shot noise match semiclassical predictions.

Conductance fluctuations show minimal dependence on Ehrenfest time.

Quantum effects are delayed as a function of Ehrenfest time.

Abstract

We investigate the behavior of weak localization, conductance fluctuations, and shot noise of a chaotic scatterer in the semiclassical limit. Time resolved numerical results, obtained by truncating the time-evolution of a kicked quantum map after a certain number of iterations, are compared to semiclassical theory. Considering how the appearance of quantum effects is delayed as a function of the Ehrenfest time gives a new method to compare theory and numerical simulations. We find that both weak localization and shot noise agree with semiclassical theory, which predicts exponential suppression with increasing Ehrenfest time. However, conductance fluctuations exhibit different behavior, with only a slight dependence on the Ehrenfest time.