Multiphonon decay of strong mode in quantum lattice

Abstract

A nonperturbative theory of multiphonon anharmonic decay of strongly excited local mode is developed whereby the mode is considered classically and phonons, quantum mechanically. The decay rate of the mode is expressed via the negative frequency parts of the phonon pair correlation functions. In the case of two-phonon decay the later satisfy the linear integral equations while in the case of two- and more-phonon decay they satisfy the nonlinear integral equations. As a result, the processes mentioned differently depend on the mode amplitude A: two-phonon processes smoothly deminish if A tends to infinity while three- and more-phonon processes are fully switched-off at large amplitudes and they abruptly switch-on if the amplitude approaches the critical value. At that the decay rate gets rather high value (of the order of the mode quantum per period). The final stage of the relaxation is well described by the perturbation theory.