Localization for one-dimensional random potentials with large local fluctuations

Abstract

We study the localization of wave functions for one-dimensional Schrödinger Hamiltonians with random potentials $V(x)$ with short range correlations and large local fluctuations such that $\int\D{x} \smean{V(x)V(0)}=\infty$. A random supersymmetric Hamiltonian is also considered. Depending on how large the fluctuations of $V(x)$ are, we find either new energy dependences of the localization length, $\ell_\mathrm{loc}\propto{}E/\ln{E}$, $\ell_\mathrm{loc}\propto{}E^{μ/2}$ with $0<μ<2$ or $\ell_\mathrm{loc}\propto\ln^{μ-1}E$ for $μ>1$, or superlocalization (decay of the wave functions faster than a simple exponential).

9 pages, LaTeX, 2 eps figures ; v2: Refs. added, small paragraph added p.4, additional table in conclusion