SEMICLASSICAL STUDY OF THE COLLECTIVE OSCILLATION AND FLUCTUATION OF FINITE QUANTUM SYSTEMS

在有限量子多体系统中，如被困在势中的原子核或冷原子气体，已经观察到各种类型的集体激发。在许多情况下，这些激发态的体积性质是由服从经典动力学的集体变量来描述的。进一步的性质，如强度函数的波动，可以在裸状态下观察到，这可能与经典系统的非线性特性有关。在本研究中，采用上述两种系统以及为波函数的特定结构提供模型的一种更简单的系统来研究这些性质。原子核中的巨共振和强度函数的波动我们考虑了几种不同的方法来表征集体激励强度函数的波动。特别以巨型四极共振为例，对强度函数精细结构的分形维数进行了研究。我们认为，分形维数对能量尺度的依赖性可能包含了基本激发机制的门道结构信息。在冷原子气体中被困在一个潜在的集体振荡的半经典研究也被发现，尽管详细的光谱研究仍有待完成。我们用RPA方法研究了玻色-费米混合物中的各种振荡，并与半经典方法进行了比较。我们特别研究了排斥系统的等矢量单极子型振荡，并分析了相分离的不稳定性。2维不可积系统的节点域分布量子系统的波函数可以以不同的方式反映相应经典系统的不可积性。我们考虑了二维非谐振子模型中的节点域结构。我们发现在节点域的分布从可积系统到混沌系统的转变不是单调的，而是与非线性参数有特征依赖。少

Various types of collective excitations have been observed in finite quantum many-body systems such as nuclei or cold atomic gasses trapped in a potential. Bulk properties of these excitations are in many cases described by collective variables which obey classical dynamics. Further properties such as fluctuations in the strength functions are observed in nude, which may be related to non-linear properties characteristic to classical systems. In the present research, these properties have been studied by adopting the above two systems as well as a simpler system which provides a model for a specific structure of wave functions.1) Giant Resonaces in Nuclei and the Fluctuations in the Strength FunctionWe considered several different measures to characterize fluctuations in the strength function of collective excitations. In particular, the fractal dimensions obtained from the fine structure of strenth functions were studied, using as an example the giant quadrupole resonances. We suggest … More ed that the dependence of the fractal dimension on the energy scale may contain the information on the doorway structure of the basic excitation mechanism.2) Semiclassical Study of collective oscillations in cold atomic gases trapped in a potentialCollective oscillations have also been found here albeit the detailed spectroscopic studies are still to be done. We studied various oscillations in bose-fermi mixture using RPA and compared results with semiclassical method. We studied in particular the isovector monopole type oscillation for repulsive systems and made analysis of the instability towards phase separation.3) Nodal Domain Distribution in the Two-dimensional Nonintegrable SystemsThe wave functions of quantum systems may reflect in various ways the nonintegrability in the corresponding classical systems. We considered nodal domain structures in the two- dimensional anharmonic oscillator model. We found that the transition in the nodal domain distirubtions from integrable to chaotic systems is not monotonic but has a characteristic dependence on the nonlinear parameter. Less