New Theory of Superconductivity. Method of Equilibrium Density Matrix. Magnetic Field in Superconductor

A new variational method has been proposed for studying the equilibrium states of the interacting particle system to have been statistically described by using the density matrix. This method is used for describing conductivity electrons and their behavior in metals. The electron energy has been expressed by means of the density matrix. The interaction energy of two ε_kk’ electrons dependent on their wave vectors k and k’ has been found. Energy ε_{k k’} has two summands. The first energy I summand depends on the wave vectors to be equal in magnitude and opposite in direction. This summand describes the repulsion between electrons. Another energy I summand describes the attraction between the electrons of equal wave vectors. Thus, the equation of wavevector electron distribution function has been obtained by using the variational method. Particular solutions of the equations have been found. It has been demonstrated that the electron distribution function exhibits some previously unknown features at low temperatures. Repulsion of the wave vectors k and ﹣k electrons results in anisotropy of the distribution function. This matter points to the electron superconductivity. Those electrons to have equal wave vectors are attracted thus producing pairs and creating an energy gap. It is considered the influence of magnetic field on the superconductor. This explains the phenomenon of Meissner and Ochsenfeld.