Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2005-07-22
Phys. Rev. E 72, 036214 (2005)
Nonlinear Sciences
Chaotic Dynamics
13 pages, 6 figures, submitted to Phys Rev E
Scientific paper
10.1103/PhysRevE.72.036214
We examine spectral equilibration of quantum chaotic spectra to universal statistics, in the context of the Brownian motion model. Two competing time scales, proportional and inversely proportional to the classical relaxation time, jointly govern the equilibration process. Multiplicity of quantum systems having the same semiclassical limit is not sufficient to obtain equilibration of any spectral modes in two-dimensional systems, while in three-dimensional systems equilibration for some spectral modes is possible if the classical relaxation rate is slow. Connections are made with upper bounds on semiclassical accuracy and with fidelity decay in the presence of a weak perturbation.
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