Localization Properties in One Dimensional Disordered Supersymmetric Quantum Mechanics

A. Comtet 1, J. Desbois 1, C. Monthus 1

Annals of Physics 239 (1995) 312-350

A model of localization based on the Witten Hamiltonian of supersymmetric quantum mechanics is considered. The case where the superpotential $\\phi(x)$ is a random telegraph process is solved exactly. Both the localization length and the density of states are obtained analytically. A detailed study of the low energy behaviour is presented. Analytical and numerical results are presented in the case where the intervals over which $\\phi(x)$ is kept constant are distributed according to a broad distribution. Various applications of this model are considered.

  • 1. Division de Physique Théorique, IPN,
    Université Paris XI - Paris Sud