On a model for quantum friction. I. Fermi's Golden Rule and dynamics at zero temperature
Résumé
We investigate the dynamics of a quantum particle in a confining potential linearly coupled to a bosonic field at temperature zero. For a massive field we show, by employing complex deformation techniques, that Markovian semigroup which approximates the particles dynamics on the time scale $\tau=\lambda^2t$ ($\lambda$ strength of the coupling) is determined by the resonances of the full energy operator. We also show that Markovian master equation technique leads to the right prediction for the life-time of resonances. We discuss the dissipation of the particle into its ground state both in the time mean and on the above time scale.