Partial Factorization of Wave Function for A Quantum Dissipation System

The microscopic approach quantum dissipation process presented by Yu and Sun [Phys. is developed to analyze the wave function structure of dynamic evolution of a typical dissipative system, a single mode boson soaked in a bath of many bosons. In this paper, the wave function of total system is explicitly obtained as a product of two components of the system and the bath in the coherent state representation. It not only describes the influence of the bath on the variable of the system through the Brownian motion, but also manifests the back-action of the system on the bath and the effects of the mutual interaction among the bosons of the bath. Due to the back-action, the total wave function can only be partially factorizable even for the Brownian motion can be ignored in certain senses, such as the cases with weak coupling and large detuning. 1 1. Introduction: The typical microscopic treatment for the model of quantum dissi-pation is to consider a harmonic oscillator interacting with a many-oscillator bath (e.g., in [1-6]). This simple and rather conventional model has been used to completely clarify the relation between two different approaches for quantum dissipation process frequently appearing in the literature, i.e., the system plus bath model and the time-dependent effective Hamiltonian by Kanai and Calderora [7,8], since Yu and one (Sun) of the authors wrote down the total wave function explicitly in a form of direct product of the bath component and the system component [1,2]. In the discussion, because the mixed variables were chosen to describe the system and the bath, the wave function only manifested the influence of the bath on the system through the Brownian broadening of the width of the wave function for the system, but the back-action of the system on the bath was not discussed. If there indeed exists the back-action of the system on the bath, it is reasonable to expect that, for the individual particles constituting the bath, the mutual couplings among them can indirectly appear in a second order through coupling the system as an intermediate process. Another question is the relation between quantum and classical systems. In many real situations, the classical or macroscopic states can be represented by coherent states in the quantum optics and the macroscopic quantum mechanics. Therefore it is significant to study how the system with an initial coherent state evolves if it really has a macroscopic …