Nonstationary Superconductivity: Quantum Dissipation and Time-Dependent Ginzburg-Landau Equation

Transport equations of the macroscopic superfluid dynamics are revised on the basis of a combination of the conventional (stationary) Ginzburg-Landau equation and Schrodinger's equation for the macroscopic wave function (often called the order parameter) by using the well-known Madelung-Feynman approach to representation of the quantum-mechanical equations in hydrodynamic form. Such an approach has given (a) three different contributions to the resulting chemical potential mu(s) for the superfluid component, (b) a general hydrodynamic equation of superfluid motion, (c) the continuity equation for superfluid flow with a relaxation term involving the phenomenological parameters tau(GL) and xi(GL), (d) a new version of the time-dependent Ginzburg-Landau equation for the modulus of the order parameter which takes into account dissipation effects and reflects the charge conservation property for the superfluid component. The conventional Ginzburg-Landau equation also follows from our continuity equation as a particular case of stationarity. All the results obtained are mutually consistent within the scope of the chosen phenomenological description and, being model-neutral, applicable to both the low-T-c and high-T-c superconductors.