Staggered repulsion of transmission eigenvalues in symmetric open mesoscopic systems

TL;DR

This paper reveals that in symmetric open quantum systems, transmission eigenvalues exhibit staggered level repulsion, with statistical properties differing from traditional models, confirmed by numerical simulations.

Contribution

It introduces the concept of staggered eigenvalue repulsion in open systems with symmetries that interchange openings, extending random-matrix theory to these cases.

Findings

Eigenvalue statistics show level repulsion between every second eigenvalue.

The eigenvalue distribution approaches that of two uncorrelated sets for many channels.

Numerical simulations confirm the theoretical predictions.

Abstract

Quantum systems with discrete symmetries can usually be desymmetrized, but this strategy fails when considering transport in open systems with a symmetry that maps different openings onto each other. We investigate the joint probability density of transmission eigenvalues for such systems in random-matrix theory. In the orthogonal symmetry class we show that the eigenvalue statistics manifests level repulsion between only every second transmission eigenvalue. This finds its natural statistical interpretation as a staggeredsuperposition of two eigenvalue sequences. For a large number of channels, the statistics for a system with a lead-transposing symmetry approaches that of a superposition of two uncorrelated sets of eigenvalues as in systems with a lead-preserving symmetry (which can be desymmetrized). These predictions are confirmed by numerical computations of the transmission-eigenvalue spacing distribution for quantum billiards and for the open kicked rotator.