Charge-Relaxation and Dwell Time in the fluctuating Admittance of a Chaotic Cavity

TL;DR

This paper analyzes the admittance of a chaotic quantum dot, revealing that it is governed by both the RC-time and dwell time, with the latter dominating weak-localization corrections and fluctuations, using random-matrix theory.

Contribution

It introduces a statistical framework for admittance in chaotic quantum dots, highlighting the roles of RC-time and dwell time in quantum transport properties.

Findings

Admittance depends on RC-time and dwell time.

Weak-localization corrections are governed by dwell time.

Variance of admittance is characterized using random-matrix theory.

Abstract

We consider the admittance of a chaotic quantum dot, capacitively coupled to a gate and connected to two electron reservoirs by multichannel ballistic point contacts. For a dot in the regime of weak-localization and universal conductance fluctuations, we calculate the average and variance of the admittance using random-matrix theory. We find that the admittance is governed by two time-scales: the classical admittance depends on the RC-time of the quantum dot, but the relevant time scale for the weak-localization correction and the admittance fluctuations is the dwell time. An extension of the circular ensemble is used for a statistical description of the energy dependence of the scattering matrix.