Localization Properties in One Dimensional Disordered Supersymmetric Quantum Mechanics

A model of localization based on the Witten Hamiltonian of supersymmetric quantum mechanics is considered. The case where the superpotential $ϕ(x)$ 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 $ϕ(x)$ is kept constant are distributed according to a broad distribution. Various applications of this model are considered.

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