Localization for one-dimensional random potentials with large local fluctuations

Abstract

We study the localization of wavefunctions for one-dimensional Schrödinger Hamiltonians with random potentials V(x) with short-range correlations and large local fluctuations such that . 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, ℓloc ∝ E/ln E, ℓloc ∝ Eμ/2 with 0 < μ < 2 or ℓloc ∝ lnμ−1E for μ > 1, or superlocalization (decay of the wavefunctions faster than a simple exponential).