Generalization of the Poisson kernel to the superconducting random-matrix ensembles
arXiv:0902.2164 · doi:10.1103/PhysRevB.79.214506
Abstract
We calculate the distribution of the scattering matrix at the Fermi level for chaotic normal-superconducting systems for the case of arbitrary coupling of the scattering region to the scattering channels. The derivation is based on the assumption of uniformly distributed scattering matrices at ideal coupling, which holds in the absence of a gap in the quasiparticle excitation spectrum. The resulting distribution generalizes the Poisson kernel to the nonstandard symmetry classes introduced by Altland and Zirnbauer. We show that unlike the Poisson kernel, our result cannot be obtained by combining the maximum entropy principle with the analyticity-ergodicity constraint. As a simple application, we calculate the distribution of the conductance for a single-channel chaotic Andreev quantum dot in a magnetic field.
7 pages, 2 figures
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- Dephasing-enabled triplet Andreev conductance
- Random-matrix theory of thermal conduction in superconducting quantum dots
- Statistics of reflection eigenvalues in chaotic cavities with non-ideal leads
- Random matrix theory of quantum transport in chaotic cavities with non-ideal leads
- Effect of a tunnel barrier on the scattering from a Majorana bound state in an Andreev billiard
- Kuramoto variables as eigenvalues of unitary matrices