The Statistical Dynamics of a System Consisting of a Classical and a Quantum Subsystem

Abstract

Abstract For a system consisting of a quantum and a classical subsystem, an equation of the Liouville type is obtained starting with the density matrix equation. The validity condition and the transformation properties of this quantum-classical equation as well as the application of the adiabatic approximation and the perturbation theory within the frame of this equation are discussed. Some general expressions are obtained for the probability of the transition between the quasi-equilibrium states of the system. Special attention is given to the electron-nuclei system, as the general formalism was developed first of all in order to obtain a foundation for the theoretical analysis of elementary processes in liquids. An example is given to demonstrate that the quantum-classical approach in the range of its validity gives the same result as the corresponding quantum solution. It is also shown that both the cases of weak and strong interaction (leading to the transition) can be described by the quantum-classical equation in question.