Quasiclassical description of condensed systems by a complex order parameter

Abstract

A quasiclassical description of condensed systems is given in terms of a complex order parameter ψ interacting with a gauge field Aμ. The order parameter ψ can relate as to the conserving as to the non-conserving number of corresponding particles. The electromagnetic field as well as the deformation field of the specific type may take a part of the gauge Aμ-field. The phenomenological Lagrangian of the model is constructed in the coordinate representation. The parameters of the Lagrangian are expressed in terms of the medium polarization function. The transition from the given ψ order parameter to the quasiclassical variables, ∣ψ∣2 and ∇S, where ψ = ∣ψ∣eiS, is performed for the general case of the non-conserving particle number. Equations obtained are formally analogous to the Navier-Stokes equation and to the continuity equation. The latter, however, consists of some particle source in the r.h.s. The principal question on the possibility of the description of systems with dissipation in terms of macroscopic ψ-function is raised and positively solved. The transition from the obtained equations for the macroscopic wave function to the hydrodynamical variables is also performed. The first and the second viscosities are expressed in terms of the medium polarization function. It is shown that the inhomogeneous phase (k ≠ 0) is described by anisotropic hydrodynamical equations. The hydrodynamical equations are reduced to more simple equations describing the relaxation of the new order parameters. As an example, the dynamics of the non-conserving order parameter in the homogeneous system, which undergoes the first order phase transition from the metastable state to the stable one, is considered in detail. The question how the weakly non-spherical overcritical germs acquire the spherical shape during their evolution is studied. It is shown that some essentially non-spherical initial configurations have significantly smaller critical size than the spherical ones and they conserve the shape during their growth to the new phase. The static inhomogeneous configurations of the one-axis systems and the configurations of the anisotropic three-dimensional lattices are studied. The dynamics of the first order phase transition to the inhomogeneous condensed state is considered. It is shown that this dynamics is essentially anisotropic. Different initial configurations have the distinct critical sizes and their evolution is characterized by the various velocities. Achieved dynamical description allows to understand the physical picture of the process of the monocrystal and the polycrystal growth. A possible description of the glassing and amorphouzation processes as the phase transitions from the lability region to some heterogenic inhomogeneous (k ≠ 0) state is discussed. The problem of the domain sticking in the polycrystals is considered. The dynamics of the process of the material aging is also discussed in the framework of the given model.