The phase transition between ordered and disordered states is discussed within the framework of non-equilibrium Thermo Field Dynamics (TFD), in which the time-dependent thermal Bogoliubov transformation takes care of the temporal change of quasi-particles. Thus, the system, which is closed, passes through a continuum of out of equilibrium states in going from one phase to another. The formalism is presented for the superfluid model. The time evolution of the system is determined by the self-consistent renormalization conditions which give us equations for the order parameter, number distributions, dissipative coefficients and renormalized energies. A differential Ward-Takahashi relation, rather than an integral one, is combined with the renormalization condition to study the zero momentum mode.
|ジャーナル||Physica A: Statistical Mechanics and its Applications|
|出版ステータス||Published - 1989 5 15|
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