Quantum ohmic dissipation : coherence vs. incoherence and symmetry-breaking. a simple dynamical approach

By using standard quantum-statistical methods, we study the dynamics of a particle in a double-well potential, coupled dissipatively, in an « ohmic » way, to a bath of phonons. We refine previous results about the T = 0 symmetry breaking : (i) the critical behaviour of the order parameter is exhibited and the symmetry is shown to be only fully broken for infinite coupling; (ii) the dynamics follows a generalized Kohlrausch law of the type exp(- atb), where both parameters a and b are exactly calculated; a critical slowing down is very clearly displayed At finite temperature, the symmetry breaking does disappear, although a precursor behaviour of the transition exists when T → 0+. These results are extended to a particle in a multiple-well potential for which a localization phenomenon is seen to occur at T = 0. Finally, we investigate other dissipation laws (i.e. non ohmic) and we show that the ohmic model is unique by its ability to produce such a transition, although a precursor behaviour can be obtained for near-ohmic dissipation laws.