A quantum-mechanical dissipation theory is applied to the problem of anharmonic vibrations of a crystal. Equations for the anharmonic phonon creation and annihilation operators are obtained, from which may be extracted damping-constant and frequency-shift expressions. These are compared with the results of other techniques.

• Received 19 March 1968

DOI:https://doi.org/10.1103/PhysRev.172.640