Large-N expansion for the time-delay matrix of ballistic chaotic cavities

2016/07/31 by Fabio Deelan Cunden, Francesco Mezzadri, Nick Simm +1 · 1 citation
Mathematics · Physics and Astronomy · #cond-mat.mes-hall #cond-mat.stat-mech #math-ph #math.MP

paper · pdf · doi:10.1063/1.4966642

published as J. Math. Phys. 57, 111901 (2016) · 26 pages, 1 table. Final version

arxiv created 2016/10/27 · arxiv updated 2016/11/09

Abstract

We consider the 1/N-expansion of the moments of the proper delay times for a ballistic chaotic cavity supporting N scattering channels. In the random matrix approach, these moments correspond to traces of negative powers of Wishart matrices. For systems with and without broken time reversal symmetry (Dyson indices β=1 and β=2) we obtain a recursion relation, which efficiently generates the coefficients of the 1/N-expansion of the moments. The integrality of these coefficients and their possible diagrammatic interpretation is discussed.

Cited by

• Random Matrix Theory for Chaotic Wave Scattering and Transport

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