FLUCTUATION PROPERTIES OF STRENGTH FUNCTIONS IN NONLINEAR SYSTEMS

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The purpose of the present investigation is to study fluctuation properties of the strength functions which appear when some parent state (s) is embedded in a vast number of background states. We studied several model systems and calculated various signatures which measure fluctuation of the strength function.We first considered a model which consists of a single parent state (supposedly a collective state) and a background states, the latter being taken as the two-dimensional anharmonic oscillator. The dynamical characteristics of this oscillator system is known to show regular as well as chaotic properties as a function of a single parameter. The coupling between the parent state and the background system has been taken to be a simple form so as to isolate the effects of the background system. We studied energy-moments, strength distribution, fractal dimensions and the survival probability (Fourier transform) for the strength function. It was found that the strength distribution and the survival probability are sensity to the dynamical character of the background system, while the energy moments are not much dependent on the latter being constrained by sum rules. The fractal dimension, too, is insensitive to the parameter of the background system. It takes, however, a different value from that obtained for a background system constructed from random matrix, and thus may be a signature of another character.We then considered a model where two parent states couple to the same backround system. Here it is possible to study (in) coherence of the two parent states as a result of the coupling. We calculated energies and strength functions as function of the energy difference between the parent states. It was shown that the behavior of the main strength is quite different for a regular or a chaotic background system. A further study is being performed from the standpoint of the level dyanmics.