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

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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