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

We propose a class of exactly solvable anisotropic tight-binding models on an infinite-dimensional hypercube. The energy spectrum is computed analytic ally and is shown to be fractal and/or absolutely continuous according to t he value of the hopping parameters. In both cases, the spectral and diffusi on exponents are derived. The main result is that, even if the spectrum is absolutely continuous, the diffusion exponent for the wave packet may be an ything between 0 and 1 depending upon the class of models.