Research for Many-Dimensional Quantum and Classical Chaos

一曰：多维量子混沌的研究--本研究的目的是阐明在低维量子混沌系统中被破坏的量子-经典对应是否随着自由度的增加而恢复。强有力的数字证据表明，Q.C.具有3个以上自由度的系统可以有条件地表现出轨道不稳定性，这是混沌动力学的本质根源。建立了经典混沌行为恢复的一般判据。通过对Q.C. systeras，我们提出了数字“严格”的证据表明，Q.C.可以是一个起源的耗散。2：研究多维耗散混沌--信息理论方法的发展，并被证明是非常强大的动力学结构的描述复杂的湍流行为的无限自由度的系统。我们将这种方法应用于光学湍流、化学湍流等各种系统的模拟研究中，发现一种我们称之为混沌巡游的特征现象在弱湍流发展为强湍流的过程中起着重要的作用。信息论方法在流体湍流研究中的应用正在发展。

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.