From Coherent State Statistics to the Frozen Phonon Model

We present a formalism for employing the basis of coherent states for analytical and numerical computations involving systems at thermal equilibrium. We identify an integration measure on the complex plane which may be understood as the weight function for a thermal distribution of coherent states. When applied to phonons in a thermally occupied harmonic crystal, this method yields an intuitive and rigorously quantum mechanical justification of the frozen phonon model of thermal diffuse scattering. In this and many other applications, the semiclassical dynamics of coherent states can mediate the application of classical reasoning to otherwise intractable quantum problems, including those involving anharmonic potentials. We also discuss and refine the concept of “quasi-elastic” scattering.