Localization for one-dimensional random potentials with large local fluctuations

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

2008-07-04

arxiv.org/abs/0807.0772v2

J. Phys. A: Math. Theor. 41 (2008) 475001

Physics

Condensed Matter

Disordered Systems and Neural Networks

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

Scientific paper

10.1088/1751-8113/41/47/475001

We study the localization of wave functions for one-dimensional Schr\"odinger 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).

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