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波动特性。我们研究了几个模型系统，并计算了测量强度函数波动的各种特征。我们首先考虑了一个由单亲状态（假定是集体状态）和背景状态组成的模型，后者被视为二维非谐振子。已知该振子系统的动态特性作为单一参数的函数既具有规则特性又具有混沌特性。父状态和后台系统之间的耦合被采取一种简单的形式，以隔离后台系统的影响。我们研究了能量矩、强度分布、分形维数和强度函数的生存概率（傅里叶变换）。研究发现，强度分布和生存概率对背景系统的动态特性比较敏感，而能量矩受求和规则的约束，对后者的依赖性不大。分形维数对背景系统参数也不敏感。然而，它取的值与从随机矩阵构造的背景系统得到的值不同，因此可能是另一个字符的签名。然后我们考虑了一个模型，其中两个父状态与相同的背景系统耦合。在这里，可以研究由于耦合而产生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能量差的函数。结果表明，在规则背景系统和混沌背景系统中，主强度的行为有很大的不同。目前正在从水平动力学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.