Semiclassical approach to universality in quantum chaotic transport

Abstract

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

Published version. Changes in presentation

References in corpus (7)

• Periodic-Orbit Theory of Universality in Quantum Chaos
• Semiclassical Theory of Chaotic Conductors
• Semiclassical Approach to Chaotic Quantum Transport
• Statistics of quantum transport in chaotic cavities with broken time-reversal symmetry
• Ehrenfest-time dependence of weak localization in open quantum dots
• Full counting statistics of chaotic cavities from classical action correlations
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