FLUCTUATION PROPERTIES OF STRENGTH FUNCTIONS IN NONLINEAR SYSTEMS

本研究的目的是研究当某些母态嵌入大量背景态时强度函数的涨落性质。我们研究了几个模型系统，计算了各种测量强度函数涨落的信号，首先考虑了一个由单个母态（假定是集体态）和一个背景态组成的模型，背景态被看作是二维非谐振子。已知该振荡器系统的动力学特性显示作为单个参数的函数的规则以及混沌特性。母态和背景系统之间的耦合被视为一种简单的形式，以隔离背景系统的影响。我们研究了能量矩，强度分布，分形维数和生存概率（傅立叶变换）的强度函数。结果表明，强度分布和生存概率对背景系统的动力学性质敏感，而能量矩对受求和规则约束的背景系统的动力学性质的依赖性不大。分形维数对背景系统的参数也不敏感。然而，它的值与由随机矩阵构成的背景系统的值不同，因此它可能是另一个特征的信号。然后我们考虑了两个母态耦合到同一个背景系统的模型。在这里，可以研究作为耦合结果的两个母态的相干性。我们计算了能量和强度函数作为母态之间的能量差的函数。结果表明，对于规则背景系统和混沌背景系统，主强度的行为是完全不同的。目前正在从各级政府的角度进行进一步的研究。

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.