Nonlinear quantum dynamics of strong vibration: relaxation jumps and phonon bursts

Abstract

We examine quantum decay of localized vibrations in anharmonic crystal lattice. The theory which describes two-phonon anharmonic relaxation can be applied both to local modes associated with substitutional impurity and to intrinsic local modes (ILM) in perfect lattices. It is found that for sufficiently high initial excitations relaxation of vibrations is non-exponential, it demonstrates explosion-like behavior at specific stages of evolution. The course of the relaxation is determined by the initial value of energy, temperature, direction of vibrations. As an example we present the results of calculations of the relaxation of an odd local (impurity) mode in a simple cubic lattice and discuss the influence of quantum fluctuations on the stability of the ILM in one-dimensional monatomic chain.