Collision-broadened phonon line shape in the overdamped or hydrodynamic regime

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Abstract
It can be shown that if amplitude as well as momentum changes during phonon scattering events are taken into account, the line shape associated with infrared- or Raman-active lattice modes can be of the Lorentz or Van Vleck-Weisskopf form as well as of the damped-oscillator form. An expression is derived for the susceptibility of an active mode of an anharmonic lattice. This expression reduces to the damped-oscillator form in the collisionless regime and to the Van Vleck-Weisskopf form in the collision-dominated regime. It is emphasized that such considerations should be important in the vicinity of a second-order phase transition where an active-mode frequency becomes anomalously low and the mode becomes overdamped.

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