Wavefunction extreme value statistics in Anderson localization
| Autor: | Falcão, P. R. N., Lyra, M. L. |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevB.106.184207 |
| Popis: | 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. Comment: 8 pages, 8 figures |
| Databáze: | arXiv |
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