The Phase Transition to an Inhomogeneous Condensate State

Abstract

The Lagrangian (free energy) of the model with a complex scalar order parameter in which the phase transition to an inhomogeneous condensate state exists is constructed in the coordinate representation. In the case of condensation of charged particles (for example paired electrons) interaction with the electromagnetic field is included. The excitation spectrum in the presence of the condensate is found. The oscilations are strongly anisotropic. It is shown that superfluidity is absent for an uncharged system but that the charged one has the property of superconductivity. The important role of thermal fluctuations is demonstrated. They drastically change the behaviour of the condensate system. The condensation in a finite system is considered. A study is carried out for the behaviour of an inhomogeneous condensate in magnetic field. It is shown that the inhomogeneous condensate is a type II superconductor with Ginzburg-Landau paramerter κ ≫ 1, but that the structure of the mixed state of the system is unusual - consisting of plane layers of the normal phase, when Hc1 < H < H'c2. The distribution of condensate in the strong magnetic field H'c2 < H < Hc2 is also studied.