One-Dimensional Disordered Supersymmetric Quantum Mechanics: A Brief Survey

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.

16 pages, LaTeX, contribution to the proceedings of the workshop "Supersymmetry and Integrable Models", version 2: prefactor of eq.(17) corrected

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Cited by in corpus (9)

• Lyapunov exponents, one-dimensional Anderson localisation and products of random matrices
• Products of random matrices and generalised quantum point scatterers
• Fluctuations of random matrix products and 1D Dirac equation with random mass
• Supersymmetric quantum mechanics with Levy disorder in one dimension
• Effect of boundaries on the spectrum of a one-dimensional random mass Dirac Hamiltonian
• The KPZ equation in a half space with flat initial condition and the unbinding of a directed polymer from an attractive wall
• Fluctuations of the product of random matrices and generalized Lyapunov exponent
• Breaking supersymmetry in a one-dimensional random Hamiltonian
• Localization length of the $1+1$ continuum directed random polymer