The existence of a charge-induced instability is well known for the 4 He crystal surface in the rough state. Much less is known about the charge-induced instability at the 4 He crystal surface in the smooth well-faceted state below the roughening transition temperature. To meet the lack, we examine here the latter case. As long as the electric field normal to the crystal facet is below the critical value the same as for the rough surface, the crystal faceting remains absolutely stable. Above the critical field, unlike the absolutely unstable state of the rough surface, the crystal facet crosses over to the metastable state separated from the crushed state with a potential barrier proportional to the square of the linear facet step energy. The onset and development of the instability at the charged crystal facet has much in common with the nucleation kinetics of first-order phase transitions. Depending on the temperature, the electric breaking strength is determined either by thermal activation at high temperatures or by quantum tunneling at sufficiently low temperatures.

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The dissipative dynamics of a Josephson junction in the Bose-gases is considered within the framework of the model of a tunneling Hamiltonian. The effective action which describes the dynamics of the phase difference across the junction is derived using functional integration method.The dynamic equation obtained for the phase difference across the junction is analyzed for the finite temperatures in the low frequency limit involving the radiation terms. The asymmetric case of the Bose-gases with the different order parameters is calculated as well.