Spectrum and diffusion for a class of tight-binding models on hypercubes

Details Spectrum and diffusion for a class of tight-binding models on hypercubes Spectrum and diffusion for a class of tight-binding models on hypercubes

1998-11-23

arxiv.org/abs/cond-mat/9811323v1

J. Phys. A 32, 2361 (1999)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

5 pages Latex

Scientific paper

10.1088/0305-4470/32/12/009

We propose a class of exactly solvable anisotropic tight-binding models on an infinite-dimensional hypercube. The energy spectrum is analytically computed and is shown to be fractal and/or absolutely continuous according to the value 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.

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