Non-equilibrium quantum dynamics of lattice vibrations
Yamen Hamdouni, F. Benrachi · Journal of Physics A Mathematical and Theoretical · 2013
The problem of the quantum description of the damping of a 1D chain of coupled oscillators with periodic boundary conditions in the Markovian regime is solved. The equations of motion of the normal modes are derived, and the evolution in time of their mean values and variances is explicitly studied. Furthermore, we investigate the effect of the diffusion and the friction on the dynamics of the chain. It is shown that when the off-diagonal elements of the diffusion and friction tensors are taken into account, the most notable contribution of these processes is observed in the mode in which all the oscillators undergo an in-phase vibration.