Quantum dissipation: Dynamics of a particle in a symmetric double well in the presence of non-ohmic friction

We investigate the equilibrium value and the approach to equilibrium of a particle in a symmetric double-well potential and subjected to dissipation, within the model of Caldeira and Leggett, Ann. Phys. (N.Y.) 149 (1983) 374, but without the ohmic assumption. For subohmic friction, the critical value of the coupling with the bath above which the particle localizes is found to be dependent on the ratio (tunnelling frequency)/(bandwidth of the bath); for an infinite bandwidth, the results given by Leggett et al., Rev. Mod. Phys. 59 (1987) 1, are recovered. For superohmic dissipation, the particle never localizes and its coordinate always goes to zero by following, at large times, a power law in time of the form t−ν; the exponent ν is shown to have a non-intuitive variation as a function of the non-ohmicity.