Research for Many-Dimensional Quantum and Classical Chaos

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1 : Study of many-dimensional quantum chaos--The aim of the present research is to elucidate whether quantum-classical correspondence violated in low-dimensional quantum chaos (Q.C) system is restored with an increase in the number of degrees of freedom. Strong numerical evidences that Q.C. system with more than 3 degrees of freedom can exhibit, though conditionally, the orbital instability that is the essential origin chaotic dynamics. General criterion for the restoration of classical chaotic behavior is established. Through a study of light absorption by Q.C. systeras, we presented numerically "rigorous" evidences showing that Q.C. can be an origin of dissipation.2 : Study of many-dimensional dissipative chaos--An information theoretical method is developed and is shown to be very powerful in characterizing the dynamical structure of complex turbulent behavior in systems of infinite degrees of freedom. We applied this method to the study of various systems modeling optical turbulence, chemical turbulence and so on, and we discovered that a characteristic phenomenon we call (chaotic itinerancy) plays an important role in the process through which a weak turbulence grows into a strong one. Application of the information theoretical method to the study of the fluid turbulence is now being developed.