Statistics of reflection eigenvalues in chaotic cavities with non-ideal leads

TL;DR

This paper derives the probability density function of reflection eigenvalues in chaotic cavities with non-ideal leads, analyzing their statistical properties and conductance fluctuations under broken time-reversal symmetry.

Contribution

It introduces a joint probability density function for reflection eigenvalues in chaotic cavities with non-ideal leads, extending the understanding of their statistical behavior.

Findings

Derived the joint probability density function of reflection eigenvalues.

Calculated density and correlation functions of reflection eigenvalues.

Analyzed conductance fluctuations in asymmetric chaotic cavities.

Abstract

The scattering matrix approach is employed to determine a joint probability density function of reflection eigenvalues for chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Derived under assumption of broken time-reversal symmetry, this result is further utilised to (i) calculate the density and correlation functions of reflection eigenvalues, and (ii) analyse fluctuations properties of the Landauer conductance for the illustrative example of asymmetric chaotic cavity. Further extensions of the theory are pinpointed.