Distributions of Conductance and Shot Noise and Associated Phase Transitions

Pierpaolo Vivo ¹, Satya N. Majumdar ², Oriol Bohigas ²

Physical Review Letters 101 (2008) 216809

For a chaotic cavity with two indentical leads each supporting N channels, we compute analytically, for large N, the full distribution of the conductance and the shot noise power and show that in both cases there is a central Gaussian region flanked on both sides by non-Gaussian tails. The distribution is weakly singular at the junction of Gaussian and non-Gaussian regimes, a direct consequence of two phase transitions in an associated Coulomb gas problem.

• 1. The Abdus Salam International Centre for Theoretical Physics,
  ICTP Trieste
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
  CNRS : UMR8626 – Université Paris XI – Paris Sud