Random matrix theory of quantum transport in chaotic cavities with non-ideal leads

TL;DR

This paper derives the joint probability density function of reflection eigenvalues in chaotic cavities with non-ideal leads, revealing their determinantal or Pfaffian structure depending on symmetry, and applies this to entanglement production analysis.

Contribution

It provides a new analytical framework for the joint probability density of reflection eigenvalues in chaotic cavities with non-ideal leads, including explicit formulas and symmetry classifications.

Findings

Reflection eigenvalues form a determinantal ensemble at β=2.

Reflection eigenvalues form a Pfaffian ensemble at β=4.

Derived an explicit expression for the concurrence distribution in entanglement production.

Abstract

We determine the joint probability density function (JPDF) of reflection eigenvalues in three Dyson's ensembles of normal-conducting chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Expressing the JPDF in terms of hypergeometric functions of matrix arguments (labeled by the Dyson index $\beta$), we further show that reflection eigenvalues form a determinantal ensemble at $\beta=2$ and a new type of a Pfaffian ensemble at $\beta=4$. As an application, we derive a simple analytic expression for the concurrence distribution describing production of orbitally entangled electrons in chaotic cavities with tunnel point contacts when time reversal symmetry is preserved.