On the distribution of the Wigner time delay in one-dimensional disordered systems

Alain Comtet ^1, 2, Christophe Texier ²

Journal of Physics A 30 (1997) 8017-8025

We consider the scattering by a one-dimensional random potential and derive the probability distribution of the corresponding Wigner time delay. It is shown that the limiting distribution is the same for two different models and coincides with the one predicted by random matrix theory. It is also shown that the corresponding stochastic process is given by an exponential functional of the potential.

• 1. Division de Physique Théorique, IPN,
  Université Paris XI – Paris Sud
• 2. LPTPE,
  Université Paris VI – Pierre et Marie Curie