Divergence of the Classical trajectories and Weak Localization

TL;DR

This paper investigates how classical chaos, characterized by the Lyapunov exponent, influences quantum interference effects like weak localization in electron transport, revealing a delay related to the Ehrenfest time.

Contribution

It demonstrates that the weak localization correction is delayed by the Ehrenfest time, linking classical chaos parameters to quantum transport measurements.

Findings

Weak localization correction is delayed by the Ehrenfest time.

Lyapunov exponent can be inferred from frequency or temperature dependence of WLC.

Ehrenfest time exceeds transport lifetime in the semiclassical regime.

Abstract

We study the weak localization correction (WLC) to transport coefficients of a system of electrons in a static long-range potential (e.g. an antidot array or ballistic cavity). We found that the weak localization correction to the current response is delayed by the large time $t_E = \lambda^{-1} |\ln \hbar|$, where $\lambda$ is the Lyapunov exponent. In the semiclassical regime $t_E$ is much larger than the transport lifetime. Thus, the fundamental characteristic of the classical chaotic motion, Lyapunov exponent, may be found by measuring the frequency or temperature dependence of WLC.