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A brief review of studies on the dynamic process of thermal expansion since the eighties is given. A magnitude of difference of one to two orders between the results of theoretical calculations and experimental observations of the characteristic time is discussed. The nonequilibrium localized phonon gas in a ''hot spot'' is studied using the Boltzmann equation, leading to 2 soliton-like solution. It gives the way to fill the gap of the above-mentioned difference between theory and experiment. The lattice relaxation of a laser rod is developed theoretically and verified experimentally. Different expansion processes of a high-T-c superconductor below and above T-c imply the existence of some new features of excitons in the high-T-c state.

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