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

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.

published version

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• Integrable Aspects of Universal Quantum Transport in Chaotic Cavities
• Klein Paradox in Chaotic Dirac Billiards
• Kuramoto variables as eigenvalues of unitary matrices
• Exponentially small quantum correction to conductance
• Entanglement Distribution Statistic in Andreev Billiards
• Quantum transport in chaotic cavities with tunnel barriers
• Electronic transport in three-terminal chaotic systems with a tunnel barrier