CORRESPONDENCE OF ANHARMONIC LOCALIZED VIBRATIONS TO N-PHONON BOUND-STATES

A discussion of the interrelation of anharmonic localized modes and th eir quantum-mechanical analogs, the so-called N-phonon bound states, i s presented. For small systems and moderate quantum numbers, the ''exa ct'' eigenvalue spectrum is obtained by direct numerical diagonalizati on. A variational ansatz is presented which allows one to estimate ana lytically the energy levels of strongly anharmonic systems, exemplifie d here by a single quartic oscillator and a dimer model. It is shown t hat expectation values and level spacings for N-phonon bound states ar e in close agreement with estimates derived from the classical anharmo nic localized vibrations. Finally, an estimate is given for the action of anharmonic localized modes in infinite higher-dimensional systems. This estimate suggests a threshold for anharmonic localized mode exis tence in three-dimensional lattices.