Integrable theory of quantum transport in chaotic cavities

TL;DR

This paper demonstrates that quantum transport in chaotic cavities with broken time-reversal symmetry is integrable, enabling exact calculations of conductance distributions and revealing non-Gaussian features in large mode limits.

Contribution

It introduces an integrable framework for quantum transport in chaotic cavities, linking conductance statistics to Painlevé transcendents and Toda lattice equations.

Findings

Exact conductance cumulants and distributions derived

Distribution exhibits long exponential tails at large mode numbers

Framework connects quantum transport to integrable systems

Abstract

The problem of quantum transport in chaotic cavities with broken time-reversal symmetry is shown to be completely integrable in the universal limit. This observation is utilised to determine the cumulants and the distribution function of conductance for a cavity with ideal leads supporting an arbitrary number $n$ of propagating modes. Expressed in terms of solutions to the fifth Painlev\'e transcendent and/or the Toda lattice equation, the conductance distribution is further analysed in the large-$n$ limit that reveals long exponential tails in the otherwise Gaussian curve.