Quantum crystal with jumps of particles

The relation between quasi-averages and averages in the case of spontaneous breakdown of translational symmetry is analysed. A hybrid system with virtual breakdown and restoration of translational symmetry is examined. The definitions of phase probabilities and phase transitions are given. The probabilities of the formation of the localized and nonlocalized phases are found and the existence of solid-liquid phase transition is proved. The calculated melting temperatures of the crystals of the inert group are in good agreement with experimental data. The collective excitation spectrum of the hybrid crystal is determined. An explanation of the high temperature anomaly of the specific heat in crystalline helium is proposed.