A Derivation of Generalized Semi-Classical Langevin Equations Based on the Feynman Path-Integral Approach. II. The Langevin Equations in the Canonical Form

Abstract

In a previous paper a new derivation of the Langevin equations for a system coupled with a heat reservoir was given based on the Feynman path-integral representation of the transition probability, i.e. the diagonal part of a reduced density matrix of the system. The derived Langevin equations are of the form of the Lagrangian equations of motion. In this article the temporal change of the reduced density matrix as a whole, or more precisely of the Wigner phase-space distribution, is treated, and the Langevin equations equivalent to those mentioned above but in the form of the canonical equation of motion are derived in the second order perturbational approximation with respect to interactions between the system and the reservoir.