1998/11/23 by J. Vidal, Julien Vidal, Rémy Mosseri +3 · 7 citations
Mathematics · Physics and Astronomy · #Absolute continuity #Anisotropy #Class (philosophy) #Complex Network Analysis Techniques #Diffusion #Exponent #Fractal #Graph theory and applications #Hypercube #Spectral density #Spectrum (functional analysis) #Theoretical and Computational Physics #cond-mat.mes-hall
paper · pdf · doi:10.1088/0305-4470/32/12/009
published in Journal of Physics A Mathematical and General 32(12), 2361-2367 (Institute of Physics) · 5 pages Latex
arxiv created 1998/11/23 · openalex publication_date 1999/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We propose a class of exactly solvable anisotropic tight-binding models on an infinite-dimensional hypercube. The energy spectrum is computed analytically and is shown to be fractal and/or absolutely continuous according to the value of the hopping parameters. In both cases, the spectral and diffusion exponents are derived. The main result is that, even if the spectrum is absolutely continuous, the diffusion exponent for the wave packet may be anything between 0 and 1 depending upon the class of models.