  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.
