SELF-ORGANIZATION OF DISSIPATION IN CLASSICALLY CHAOTIC QUANTUM-SYSTEMS

The purpose of the present paper is to investigate whether dissipation can be self-organized in quantum systems with a small number (precisely, equal to or greater than three) of degrees of freedom, such as nuclei, polyatomic molecules, micro-clusters, provided that the system is classically chaotic. To be more concrete we examine the above problem in the context of the light absorption process. The paper is composed of three parts as follows: First, numerically computable models representing multi-dimensional (more than 2) classically chaotic quantum systems with which the whole process of light absorption experiment can be simulated are proposed. The main part of our model is equivalent to a quantum map defined on a torus and it is coupled with a small number of linear oscillators. The former, which is called the host system, models the "bright mode" and is directly coupled by a light field with an effective ground state set outside of the system, while the latter oscillators, called the helper modes, represent the "dark modes" which form an environment of the host. Second, a simulation of light absorption is carried out with the above models, and it reveals that dissipation characterized by stationary light absorption is realized through a phase transition if and only if the system is classically chaotic. In the dissipative state the absorption spectrum becomes mainly composed of a continuous component. It is further accompanied by an anomalous quantum component with a fractal peak structure, which can never be decomposed into a line spectrum at any higher resolution. A relationship between the appearance of dissipation and unidentifiability of spectral peak positions is suggested, and the effect of finite dimensionality of the Hilbert space on dissipation is also discussed. Third, a semiclassical theory of multidimensional quantum map system based upon the path-integral method is developed, and it is applied to the light absorption problem. It turns out that the semiclassical theory can precisely describe the fully dissipative state. Moreover, the semiclassical theory provides a natural basis for the interpretation of the transition to the dissipative state in terms of a competition between a remarkable growth of correlation among an exponentially increasing number of classical trajectories and a correlation-canceling mechanism originated from short-time-scale chaotic fluctuations fed back to the host system through the helper modes. This interpretation leads to a qualitative explanation of the spectral features in the fully dissipative regime. © 1993 Academic Press, Inc.