Multi-quanta energy relaxation in a nonlinear quantum dimer coupled to a phonon bath

A quantum kinetic equation is established for describing the vibrational dynamics of a nonlinear quantum dimer coupled to a phonon bath. It is shown that a critical value of the number of quanta discriminates between two dynamical regimes for the population difference of quanta between the two sites of the dimer. Below the critical value, the population difference shows low-frequency damped oscillations revealing a coherent energy transfer associated to the delocalization of a V-quanta bound state. Nevertheless, these oscillations decay due to the coupling with the phonon bath so that the dimer reaches an equilibrium configuration in which the population is uniformly distributed over the two sites. In addition, its exponential decay supports a small amplitude high frequency modulation in the short time limit. Above the critical value, the population difference is almost constant in the short time limit although it still supports a small amplitude high-frequency modulation. Then, in the long time limit, the coherent energy transfer has disappeared and the population difference exhibits a purely incoherent exponential decay to finally converge to the equilibrium.