Microscopic Theory for the Quantum to Classical Crossover in Chaotic Transport

TL;DR

This paper develops a semiclassical theory explaining the quantum-to-classical transition in chaotic transport, revealing how classical and quantum effects coexist and impact transport properties in chaotic cavities.

Contribution

It introduces a microscopic framework decomposing the scattering matrix into classical and quantum parts, elucidating their roles in transport and universality breakdown.

Findings

Classical contribution yields deterministic transmission eigenvalues 0 or 1.

Quantum ergodicity is confined to the stochastic subspace.

Fano factor vanishes in the deep semiclassical limit, while weak localization remains universal.

Abstract

We present a semiclassical theory for the scattering matrix ${\cal S}$ of a chaotic ballistic cavity at finite Ehrenfest time. Using a phase-space representation coupled with a multi-bounce expansion, we show how the Liouville conservation of phase-space volume decomposes ${\cal S}$ as ${\cal S}={\cal S}^{\rm cl} \oplus {\cal S}^{\rm qm}$. The short-time, classical contribution ${\cal S}^{\rm cl}$ generates deterministic transmission eigenvalues T=0 or 1, while quantum ergodicity is recovered within the subspace corresponding to the long-time, stochastic contribution ${\cal S}^{\rm qm}$. This provides a microscopic foundation for the two-phase fluid model, in which the cavity acts like a classical and a quantum cavity in parallel, and explains recent numerical data showing the breakdown of universality in quantum chaotic transport in the deep semiclassical limit. We show that the Fano factor of the shot-noise power vanishes in this limit, while weak localization remains universal.