A. Cuccoli et al., THERMODYNAMICS OF DISSIPATIVE QUANTUM SYSTEM BY EFFECTIVE POTENTIAL, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 55(5), 1997, pp. 4849-4852
Classical-like formulas are given in order to evaluate thermal average
s of observables belonging to a quantum nonlinear system with dissipat
ion described by the Caldeira-Leggett model [Phys. Rev. Lett. 46, 211
(1981); Ann. Phys. (N.Y.) 149, 374 (1983)]. The underlying scheme is t
he pure-quantum self-consistent harmonic approximation, which leads to
expressions with a Boltzmann factor involving an effective potential
and with a Gaussian average. The latter describes the effect of the fl
uctuations of purely quantum origin. As an illustration we calculate t
he coordinate probability distribution for a double-well potential in
the presence of various degrees of Ohmic dissipation.