Localization Properties in One Dimensional Disordered Supersymmetric Quantum Mechanics

TL;DR

This paper presents an exact analytical study of localization properties in a one-dimensional disordered supersymmetric quantum mechanics model, focusing on the superpotential as a random telegraph process, with implications for understanding localization phenomena.

Contribution

It provides exact solutions for localization length and density of states in a supersymmetric quantum model with a random telegraph superpotential, including low energy behavior analysis.

Findings

Exact expressions for localization length and density of states.

Detailed analysis of low energy behavior.

Numerical results for broad interval distributions.

Abstract

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.