| Abstract
| - We examine the volume of phase space sampled by a nonstationary wave packet when the spectral functionconsists of a single clump or of a series of them. The relaxation laws are expressed in terms of reduced timevariables τ, whose definition involves either the average density of states (for a single clump) or appropriatelyweighted average densities of states (when the spectrum consists of many clumps). Introducing reasonableapproximations, very simple generic relaxation laws are derived for the ratio N(τ)/N∞, which measures thefraction of available phase space that has been sampled by time τ. Under certain assumptions, these laws arefound to depend neither on the number nor on the individual features (shapes and widths) of the clumps.However, they strongly depend on the nature (regular or chaotic) of the underlying dynamics. When thedynamics is regular, the relaxation law is expressed in terms of τ-1, whereas the corresponding equation inthe chaotic limit is slightly more complicated and involves terms in τ-2 and τ-2 ln τ. Phase space is thusexplored according to essentially different relaxation laws in the regular and chaotic limits, the differencebeing appreciable during the entire relaxation. These laws reflect in the time domain the difference in thedistribution of nearest-neighbor level spacings observed in the energy domain (Poisson or Wigner statistics).
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