Signature of Chaotic Diffusion in Band Spectra

Details Signature of Chaotic Diffusion in Band Spectra Signature of Chaotic Diffusion in Band Spectra

1997-02-03

arxiv.org/abs/chao-dyn/9702002v2

Phys. Rev. E 57 (1998) 359-365

Nonlinear Sciences

Chaotic Dynamics

8 pages, REVTeX, 5 figures (eps)

Scientific paper

10.1103/PhysRevE.57.359

We investigate the two-point correlations in the band spectra of spatially periodic systems that exhibit chaotic diffusion in the classical limit. By including level pairs pertaining to non-identical quasimomenta, we define form factors with the winding number as a spatial argument. For times smaller than the Heisenberg time, they are related to the full space-time dependence of the classical diffusion propagator. They approach constant asymptotes via a regime, reflecting quantal ballistic motion, where they decay by a factor proportional to the number of unit cells. We derive a universal scaling function for the long-time behaviour. Our results are substantiated by a numerical study of the kicked rotor on a torus and a quasi-one-dimensional billiard chain.

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