Quantum hydrodynamic modes in one-dimensional polaron system

Dynamical relaxation process of one-dimensional polaron system weakly coupled with a thermal phonon field is theoretically investigated. In addition to the diffusion relaxation, we have found that there appears a new macroscopic quantum sound mode which stabilizes the wave packet of the quantum particle even under the random collision with the thermal phonon. This coherent sound mode is a new hydrodynamic mode obeying a macroscopic linear wave equation for the density of the particle, instead of wave function.