Random matrix theory of quantum transport in chaotic cavities with nonideal leads

Andrzej Jarosz,Pedro Vidal,Eugene Kanzieper

doi:10.1103/physrevb.91.180203

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.

Highlights

Phase-coherent quantum transport [1] in irregular cavities with fully chaotic classical dynamics exhibits a remarkable statistical universality [2,3]
Expressing the joint probability density function (JPDF) in terms of hypergeometric functions of matrix arguments, we further show that reflection eigenvalues form a determinantal ensemble at β = 2 and a new type of a Pfaffian ensemble at β = 4
Effect of tunnel point contacts on JPDF of reflection eigenvalues. In this Rapid Communication, we investigate the influence of nonideal couplings on statistics of reflection eigenvalues in normal-conducting chaotic cavities belonging to either of the three Dyson symmetry classes (β = 1, 2, or 4)

Summary

RAPID COMMUNICATIONS

Random matrix theory of quantum transport in chaotic cavities with nonideal leads. 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 β), we further show that reflection eigenvalues form a determinantal ensemble at β = 2 and a new type of a Pfaffian ensemble at β = 4. 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

Introduction

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