Abstract
We have theoretically investigated a long-time transport process of a quantum Brownian particle interacting with a thermal phonon field in a one-dimensional molecular chain. A kinetic equation is derived from a quantum Liouville equation in a weak-coupling case by applying a complex spectral representation of Liouvillean. Due to a characteristic Poincar\'e resonance for a quantum one-dimensional system, there are an infinite number of degeneracy for collision invariants. In the hydrodynamic situation, the degeneracy is lifted by the first order of perturbation of the flow term, resulting in a new hydrodynamic mode, i.e., quantum hydrodynamic sound mode. It is found that the time evolution of the quantum hydrodynamic sound mode obeys a macroscopic linear wave equation for the probability distribution of the quantum particle. It is remarkable that the stability of the wave packet of the sound wave increases as temperature increases. As a demonstration, the sound wave of the minimum uncertainty wave packet is theoretically analyzed.
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