Staggered repulsion of transmission eigenvalues in symmetric open mesoscopic systems

Marten Kopp, Henning Schomerus, and Stefan Rotter
Phys. Rev. B 78, 075312 – Published 14 August 2008

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 only between every second transmission eigenvalue. This finds its natural statistical interpretation as a staggered superposition 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.

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  • Received 4 June 2008

DOI:https://doi.org/10.1103/PhysRevB.78.075312

©2008 American Physical Society

Authors & Affiliations

Marten Kopp and Henning Schomerus

  • Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom

Stefan Rotter

  • Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA

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Issue

Vol. 78, Iss. 7 — 15 August 2008

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