Hybrid Schroedinger-Ginzburg-Landau (Sch-GL) approach in study of superconducting integrated structures

Abstract: Various superconducting lattices were simulated and can be treated as lattices of superconducting atoms with preimposed symmetry in 1, 2 and 3 dimensions. Hybrid Schroedinger-Ginzburg-Landau approach is based on the fact of the mathematical similarity of Ginzburg-Landau (GL) and Schroedinger formalisms. Starting from Schroedinger approach by change of term V(x)-E with term $\alpha(x)+\beta(x)|\psi(x)|^2$ we arrived at the Ginzburg-Landau equation. In the presented relaxation algorithm we use one and two dimensional ground energy solutions of Schroedinger equation and placed them as starting trial solution for GL relaxation method. In consecutive steps we increase the nonlinear term in the GL equation which results in achieving a stable approach of solution of GL equation. The obtained numerical results and used methodology form simulation platform bases for study of superconducting integrated structures that can model various superconducting devices. In general, one can model time-dependent geometry of superconducting structures.