The behavior of the order parameter close to the NS interface in an SNINS junction is considered. To this end, a linear integral equation, which is valid near the superconductor-normal metal interface, is obtained and researched. The Ginzburg-Landau equation is solved taking into account the effect of the current on the space behaviour of the order parameter. Applying the method of quasiorthogonality to asymptotics, the boundary condition for the Ginzburg-Landau equation is obtained. The calculation of the current states, which can exist in an SNINS junction is carried out. We assume the normal layer thickness to be arbitrary and the temperature to be close to critical.
Using a system of Heisenberg's equation of motion for both the normal and the anomalous correlation functions a two-fluid hydrodynamics for superfluid helium-4 was constructed. The method is based on a gradient expansion of the exact equations of motion for correlation functions about a local equilibrium together with explicit use of the local equilibrium statistical operator for superfluid helium in the frame of reference, where condensate is in the state of rest.
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