Signature of Chaotic Diffusion in Band Spectra

Abstract

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.

8 pages, REVTeX, 5 figures (eps)

References in corpus (1)

• Universal spectral properties of spatially periodic quantum systems with chaotic classical dynamics

Cited by in corpus (13)

• Classical and Quantum Hamiltonian Ratchets
• Directed Chaotic Transport in Hamiltonian Ratchets
• Periodic Chaotic Billiards: Quantum-Classical Correspondence in Energy Space
• Quantum-classical correspondence for local density of states and eigenfunctions of a chaotic periodic billiard
• Uni-directional transport properties of a serpent billiard
• Chaotic Electron Motion in Superlattices. Quantum-Classical Correspondence of the Structure of Eigenstates and LDOS
• Superdiffusion in a Honeycomb Billiard
• Diffusive transport of waves in a periodic waveguide
• Number of propagating modes of a diffusive periodic waveguide in the semiclassical limit
• Hierarchy of gaps and magnetic minibands in graphene in the presence of the Abrikosov vortex lattice
• Spectral correlations in systems undergoing a transition from periodicity to disorder
• Smoothed universal correlations in the two-dimensional Anderson model
• Spectral Statistics in Chaotic Systems with Two Identical Connected Cells