# Wigner time-delay distribution in chaotic cavities and freezing transition

### Christophe Texier 1, 2, Satya N. Majumdar 1

#### Physical Review Letters110 (2013) 250602

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.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Laboratoire de Physique des Solides (LPS)
CNRS : UMR8502 – Université Paris XI - Paris Sud