Wigner time-delay distribution in chaotic cavities and freezing transition

TL;DR

This paper derives the large deviation function for Wigner time-delay distribution in chaotic cavities with many channels, revealing a freezing transition linked to resonance effects and power-law tails.

Contribution

It introduces a Coulomb gas approach to analyze the large deviation function of Wigner time-delay, highlighting a freezing transition phenomenon.

Findings

Power law tail in time-delay distribution due to narrow resonances

Identification of a freezing transition in the Coulomb gas model

Large deviation function characterizing the distribution in the large N limit

Abstract

Using the joint distribution for proper time-delays of a chaotic cavity derived by Brouwer, Frahm & Beenakker [Phys. Rev. Lett. {\bf 78}, 4737 (1997)], we obtain, in the limit of large number of channels $N$, the large deviation function for the distribution of the Wigner time-delay (the sum of proper times) by a Coulomb gas method. We show that the existence of a power law tail originates from narrow resonance contributions, related to a (second order) freezing transition in the Coulomb gas.