Spectral signatures of chaotic diffusion in systems with and without spatial order

We investigate the two-point correlations in the spectra of extended system s exhibiting chaotic diffusion in the classical limit. in presence and in a bsence of spatial order. For periodic systems, we express the spectral two- point correlations in terms of form factors with the unit-cell index as a d iscrete spatial argument. For times below the Heisenberg time, they contain the full space-time dependence of the classical propagator. They approach constant asymptotes via a regime of quantum ballistic motion. In the opposi te regime of strong disorder with localized eigenstates. we derive a semicl assical approximation of the form factor that spans the entire transition f rom metallic to isolating behaviour. The regime of weak breaking of periodi city is accessed from the side of exact order by a perturbation theory for the sets of, without disorder, symmetry-related periodic orbits. (C) 2001 E lsevier Science B.V.All rights reserved.