On the statistics of superlocalized states in self-affine disordered potentials

dc.creatorLuck, J. M.
dc.date2004-09-06
dc.date.accessioned2026-07-07T03:00:19Z
dc.date.available2026-07-07T03:00:19Z
dc.descriptionWe investigate the statistics of eigenstates in a weak self-affine disordered potential in one dimension, whose Gaussian fluctuations grow with distance with a positive Hurst exponent $H$. Typical eigenstates are superlocalized on samples much larger than a well-defined crossover length, which diverges in the weak-disorder regime. We present a parallel analytical investigation of the statistics of these superlocalized states in the discrete and the continuum formalisms. For the discrete tight-binding model, the effective localization length decays logarithmically with the sample size, and the logarithm of the transmission is marginally self-averaging. For the continuum Schrödinger equation, the superlocalization phenomenon has more drastic effects. The effective localization length decays as a power of the sample length, and the logarithm of the transmission is fully non-self-averaging.
dc.description21 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0409117
dc.identifierhttp://arxiv.org/abs/cond-mat/0409117
dc.identifierJ. Phys. A 38 (2005) 987-1003
dc.identifierdoi:10.1088/0305-4470/38/5/002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/24791
dc.subjectStatistical Mechanics
dc.subjectDisordered Systems and Neural Networks
dc.titleOn the statistics of superlocalized states in self-affine disordered potentials
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