Dissipative quantum dynamics in a boson bath

We investigate the dynamics of a quantum particle coupled to a boson heat bath. Using a real-time path-integral formalism, we obtain the Wigner distribution of the particle in the form of a power series in the strength of the anharmonicity V0. This series is shown to converge for all V0 when t is fixed and for small V0 uniformly in t. The latter proves the convergence to equilibrium for small anharmonicities. The effects of initial conditions on the evolution are studied by explicitly considering two types of initial states: product states and mixed Gibbs states. We show that in certain cases the evolution of the mixed states which avoid many pathologies of the product states, arising from the removal of the cutoff on the frequency distribution of the bath, can be related to that of product states when the latter are started at t=-. We also solve exactly a simple stationary nonequilibrium model, a harmonic system in contact with two thermal baths, and derive an alternative criterion for a practically useful quasiclassical approximation. Finally, some connections to the Josephson junction are discussed. These include (a) the Green-Kubo-Einstein relation between the mobility and the diffusion constant of the washboard potential and (b) the time evolution of a rf superconducting quantum interference device.