New class of level statistics in quantum systems with unbounded diffusion

Abstract

We point out a new class of level statistics where the level-spacing distribution follows an inverse power law p(s)\ensuremath{\sim}${\mathit{s}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\beta}}}$, with \ensuremath{\beta}=3/2. It is characteristic of level clustering rather than level repulsion and appears to be universal for systems exhibiting unbounded quantum diffusion on 1D lattices. A relaxation of this class is met in a model of Bloch electorns in a magnetic field, where we find a purely diffusive spread of wave packets without the quantum limitations known from chaotic systems like the kicked rotator.