Intramolecular vibrational relaxation seen as expansion in phase space. 4. Generic relaxation laws for a spectroscopic clump profile

We examine the volume of phase space sampled by a nonstationary wave packet when the spectral function consists of a single clump or of a series of them. The relaxation laws are expressed in terms of reduced time variables tau, whose definition involves either the average density of states (for a single clump) or appropriately weighted average densities of states (when the spectrum consists of many clumps). Introducing reasonable approximations, very simple generic relaxation laws are derived for the ratio N(tau)/N-infinity which measures the fraction of available phase space that has been sampled by time tau. Under certain assumptions, these laws are found 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 the dynamics is regular, the relaxation law is expressed in terms of tau(-1), whereas the corresponding equation in the chaotic limit is slightly more complicated and involves terms in tau(-2) and tau(-2) ln tau. Phase space is thus explored according to essentially different relaxation laws in the regular and chaotic limits, the difference being appreciable during the entire relaxation. These laws reflect in the time domain the difference in the distribution of nearest-neighbor level spacings observed in the energy domain (Poisson or Wigner statistics).