Semiclassical approach to universality in quantum chaotic transport

TL;DR

This paper derives a semiclassical formula for quantum transport statistics in chaotic cavities, revealing universal behavior across all moments and channel configurations by linking trajectory correlations to combinatorial problems.

Contribution

It provides a novel semiclassical derivation of universal transport moments using action correlations and combinatorial mappings, extending previous results to all moments and channel numbers.

Findings

Semiclassical formula for transport moments valid for all m and channels

Universal statistical behavior in quantum chaotic transport established

Connection between trajectory correlations and combinatorial problems demonstrated

Abstract

The statistics of quantum transport through chaotic cavities with two leads is encoded in transport moments $M_m={\rm Tr}[(t^\dag t)^m]$, 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 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.