# Localization for one-dimensional random potentials with large local fluctuations

### Tom Bienaime 1, Christophe Texier 1

#### Journal of Physics A Mathematical and Theoretical 41 (2008) 475001

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, $\ell_\mathrm{loc}\propto{}E/\ln{E}$, $\ell_\mathrm{loc}\propto{}E^{\mu/2}$ with $0<\mu<2$ or $\ell_\mathrm{loc}\propto\ln^{\mu-1}E$ for $\mu>1$, or superlocalization (decay of the wave functions faster than a simple exponential).

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud