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arXiv · 0807.0772

Localization for one-dimensional random potentials with large local fluctuations

Tom Bienaime·Christophe Texier
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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).

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Tom Bienaime, Christophe Texier. 2008-10-27. Localization for one-dimensional random potentials with large local fluctuations. https://doi.org/10.1088/1751-8113/41/47/475001

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