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arXiv · 2210.06365

Wavefunction extreme value statistics in Anderson localization

P. R. N. Falcão·M. L. Lyra
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Abstract

We consider a disordered one-dimensional tight-binding model with power-law decaying hopping amplitudes to disclose wavefunction maximum distributions related to the Anderson localization phenomenon. Deeply in the regime of extended states, the wavefunction intensities follow the Porter-Thomas distribution while their maxima assume the Gumbel distribution. At the critical point, distinct scaling laws govern the regimes of small and large wavefunction intensities with a multifractal singularity spectrum. The distribution of maxima deviates from the usual Gumbel form and some characteristic finite-size scaling exponents are reported. Well within the localization regime, the wavefunction intensity distribution is shown to develop a sequence of pre-power-law, power-law, exponential and anomalous localized regimes. Their values are strongly correlated, which significantly affects the emerging extreme values distribution.

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P. R. N. Falcão, M. L. Lyra. 2022-10-12. Wavefunction extreme value statistics in Anderson localization. https://doi.org/10.1103/physrevb.106.184207

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