Introduction to Ginzburg-Landau and Gross-Pitaevskii Theories for Superconductors and Superfluids

An elementary overview is given of the most frequently used models in the theory of superfluidity and superconductivity. The Gross-Pitaevskii, Ginzburg-Landau and time-dependent Ginzburg-Landau equations are derived, and their conditions of applicability are discussed. Some applications are considered including the critical current and vortices.