Exponential sensitivity to dephasing of electrical conduction through a quantum dot

TL;DR

This paper investigates how quantum interference effects in a chaotic quantum dot's conductance are exponentially suppressed when dephasing time drops below the Ehrenfest time, confirmed through computer simulations.

Contribution

It provides the first simulation-based evidence of the exponential crossover in conductance suppression predicted by Aleiner and Larkin's theory.

Findings

Observed exponential suppression of conductance fluctuations with decreasing dephasing time.

Confirmed the crossover from power-law to exponential suppression as predicted.

Explained the absence of exponential suppression without dephasing using an effective random-matrix theory.

Abstract

According to random-matrix theory, interference effects in the conductance of a ballistic chaotic quantum dot should vanish $\propto(\tau_{\phi}/\tau_{D})^{p}$ when the dephasing time $\tau_{\phi}$ becomes small compared to the mean dwell time $\tau_{D}$. Aleiner and Larkin have predicted that the power law crosses over to an exponential suppression $\propto\exp(-\tau_{E}/\tau_{\phi})$ when $\tau_{\phi}$ drops below the Ehrenfest time $\tau_{E}$. We report the first observation of this crossover in a computer simulation of universal conductance fluctuations. Their theory also predicts an exponential suppression $\propto\exp(-\tau_{E}/\tau_{D})$ in the absence of dephasing -- which is not observed. We show that the effective random-matrix theory proposed previously for quantum dots without dephasing explains both observations.