Time development of coherent and superfluid properties in the course of a λ-transition

Abstract

The microscopic theory of the time evolution of an interacting Bose gas being cooled to the temperature Tc is presented. The considerations are based on the exact (in classical limit) equations of motion derived by Langer. It is shown that at the initial stages of relaxation the sharp peak appears at the low energy tail of the distribution function. The following time evolution of this peak leads to a delta function formation. When this peak is too narrow the Boltzmann equation is no longer applicable and one must apply the exact equations of motion or the quasi-Boltzmann equation derived in this work which takes into account the coherent effects. The evolution of the distribution function and of the energy spectrum in the system is given by the solution of the equation of motion. The development of a new phase is of explosive character and has a lot of features in common with instabilities in non-linear plasmas, optics, etc., and thus is of quite a general nature. In addition it is shown that the phenomenological models widely used for the description of the dynamics of the lambda -transition in a critical region can be derived from microscopic equations of motion.