One-Dimensional Disordered Supersymmetric Quantum Mechanics: A Brief Survey

TL;DR

This paper reviews a one-dimensional disordered supersymmetric quantum mechanics model, analyzing its spectral properties, ground state wave function statistics, and multifractal behavior, with comparisons to other off-diagonal disorder models.

Contribution

It provides a comprehensive survey of spectral and wave function properties in a supersymmetric quantum model with disorder, highlighting recent advances in understanding multifractality.

Findings

Spectral properties resemble those of off-diagonal disorder models.

Ground state wave functions exhibit multifractal behavior.

Recent results on exponential functionals of Brownian motion inform the analysis.

Abstract

We consider a one-dimensional model of localization based on the Witten Hamiltonian of supersymmetric quantum mechanics. The low energy spectral properties are reviewed and compared with those of other models with off-diagonal disorder. Using recent results on exponential functionals of a Brownian motion we discuss the statistical properties of the ground state wave function and their multifractal behaviour.