Mesoscopic Capacitors: A Statistical Analysis

TL;DR

This paper analyzes the statistical fluctuations of capacitance in mesoscopic systems using a random-matrix model, deriving analytical distributions for different universality classes and confirming results with numerical simulations.

Contribution

It introduces an analytical framework for the distribution of scattering time delays in mesoscopic capacitors across various universality classes.

Findings

Analytical distributions for scattering time delays derived for orthogonal, unitary, and symplectic classes.

Distribution results agree with numerical simulations.

Capacitance fluctuations depend on sample geometry and physical properties.

Abstract

The capacitance of mesoscopic samples depends on their geometry and physical properties, described in terms of characteristic times scales. The resulting ac admittance shows sample to sample fluctuations. Their distribution is studied here -through a random-matrix model- for a chaotic cavity capacitively coupled to a backgate: it is observed from the distribution of scattering time delays for the cavity, which is found analytically for the orthogonal, unitary, and symplectic universality classes, one mode in the lead connecting the cavity to the reservoir and no direct scattering. The results agree with numerical simulations.