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, ${\ell }_{\mathrm{loc}}\propto E/\ln E$, ${\ell }_{\mathrm{loc}}\propto E^{\mu /2}$ 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).

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

References in corpus (3)

• Anomalies and non-log-normal tails in one-dimensional localization with power-law disorder
• Statistics of quantum transmission in one dimension with broad disorder
• On the statistics of superlocalized states in self-affine disordered potentials