Mesoscopic Transport Through Ballistic Cavities: A Random S-Matrix Theory Approach

TL;DR

This paper uses a random S-matrix theory to analyze quantum interference effects on conductance in chaotic cavities, revealing universal conductance fluctuations and detailed distributions depending on the number of modes and magnetic field.

Contribution

It introduces a statistical S-matrix approach assuming circular ensembles to study conductance fluctuations and distributions in chaotic cavities.

Findings

Conductance fluctuations are universal for large N.

Full conductance distribution varies with N and magnetic field.

Differences in conductance distribution are significant at small N.

Abstract

We deduce the effects of quantum interference on the conductance of chaotic cavities by using a statistical ansatz for the S matrix. Assuming that the circular ensembles describe the S matrix of a chaotic cavity, we find that the conductance fluctuation and weak-localization magnitudes are universal: they are independent of the size and shape of the cavity if the number of incoming modes, N, is large. The limit of small N is more relevant experimentally; here we calculate the full distribution of the conductance and find striking differences as N changes or a magnetic field is applied.