Representation of Quantum Brownian Motion in the Collective Coordinate Method

We consider two explicitly solvable models of quantum random processes described by the Langevin equation, namely, those for a “free” quantum Brownian particle and for a quantum Brownian harmonic oscillator. The Hamiltonian (string) realization of the models reveals a soliton-like structure of “classical” solutions. Accordingly, the zero-mode collective coordinate method turns out to be an adequate means for describing the quantum dynamics of the models.