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

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 $\beta =1$ and $\beta =2$) 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.

26 pages, 1 table. Final version

References in corpus (3)

• Efficient semiclassical approach for time delays
• Charge fluctuations in open chaotic cavities
• Asymptotic analysis of a Selberg-type integral via hypergeometrics

Cited by in corpus (3)

• Large $N$ expansions for the Laguerre and Jacobi $\beta$ ensembles from the loop equations
• Time delay statistics for finite number of channels in all symmetry classes
• Grothendieck's Dessins d'Enfants in a Web of Dualities. III