DYNAMICS OF QUANTUM FLUCTUATIONS IN AN ANHARMONIC CRYSTAL MODEL

For a model given previously by the authors describing a structural ph ase transition we compute the q-mode critical fluctuations of momentum and displacement as a function of the critical temperatures, the wave vector q, and a fading-out external field. An explicit dependence on the rates of fading out is obtained. In order to define the critical f luctuation operators we prove a reconstruction theorem, which is of mo del-independent value. Finally we study the critical spectrum and get rigorous results on the soft modes and the central peak.