Wigner time-delay distribution in chaotic cavities and freezing transition

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.

RevTeX, 5 pages, 3 pdf figures ; v2 : Refs. added ; v3 : correction of a small error in the large deviation function $Φ_+(s)$