A semiclassical theory of the Ehrenfest-time dependence of quantum transport in ballistic quantum dots

TL;DR

This paper develops a semiclassical theory to analyze how the Ehrenfest time influences quantum transport properties, specifically weak localization and conductance fluctuations, in ballistic quantum dots with ideal contacts.

Contribution

It provides a trajectory-based semiclassical calculation revealing the Ehrenfest-time dependence of quantum corrections in ballistic quantum dots, aligning with numerical simulations.

Findings

Weak localization correction scales as exp(-tau_E/tau_D)

Conductance fluctuation variance is independent of tau_E

Results agree with previous numerical simulations

Abstract

We present a trajectory-based semiclassical calculation of the Ehrenfest-time dependence of the weak localization correction and the universal conductance fluctuations of a ballistic quantum dot with ideal point contacts. While the weak localization correction is proportional to exp(-tau_E/tau_D), where tau_E and tau_D are the dot's Ehrenfest time and dwell time, respectively, the variance of the conductance is found to be independent of tau_E. The latter is in agreement with numerical simulations of the quantum kicked rotator [Tworzydlo et al., Phys. Rev. B 69, 165318 (2004) and Jacquod and Sukhorukov, Phys. Rev. Lett. 92, 116801 (2004)].