In the present work we use nonrelativistic many body physics techniques to generalize the classical limit of quantum systems in such a way as to incorporate statistical mixtures. Finite temperature effects are thus incorporated in a natural way. We give a detailed account of the thermodynamics of the SU(3) Lipkin model and then derive the classical thermal (chaotic) dynamics of the system. The most remarkable features of our analysis are twofold: firstly the appearance of a new degree of freedom essentially connected to thermal effects, i.e., for high enough temperatures. Secondly we give a quantitative characterization of the temperature effects on the chaotic volume of the system. Thermal effects are shown to be responsible for novel nonlinear contributions to the dynamics and to consistently counterbalance the interaction part of the dynamics. This is the case in the context both of thermodynamics and of the thermal dynamics and we believe it to be true in general.
1998 Academic Press
I. INTRODUCTION
The discovery of chaotic phenomena with manifestly universal characteristics in so many different areas of science can undoubtedly be considered as one of the Article No. PH975742