2004/09/06 by J. M. Luck · 3 citations
Engineering · Physics and Astronomy · #Quantum and electron transport phenomena #Terahertz technology and applications #Topological Materials and Phenomena #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/38/5/002
published as J. Phys. A 38 (2005) 987-1003 · 21 pages, 6 figures
arxiv created 2004/09/06 · openalex publication_date 2005/01/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We 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.