Semiclassical approach to universality in quantum chaotic transport

Departamento de Física, Universidade Federal de São Carlos - São Carlos, SP, 13565-905, Brazil

^a marcel.novaes@gmail.com

Received: 25 January 2012
Accepted: 30 March 2012

Abstract

The statistics of quantum transport through chaotic cavities with two leads is encoded in transport moments M_m=Tr[(t^†t)^m], where t is the transmission matrix, which have a known universal expression for systems without time-reversal symmetry. We present a semiclassical derivation of this universality, based on action correlations that exist between sets of long scattering trajectories. Our semiclassical formula for M_m holds for all values of m and an arbitrary number of open channels. This is achieved by mapping the problem into two independent combinatorial problems, one involving pairs of set partitions and the other involving factorizations in the symmetric group.