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

Abstract

Transport equations of the macroscopic superfluid dynamics are revised on the basis of a combination of the conventional (stationary) Ginzburg-Landau equation and Schrödinger'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 μ 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 τ GL and ξ 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.

Electrically Induced Liquid–Liquid Phase Transition in a Floating Water Bridge Identified by Refractive Index Variations

“…These variations occur during the phase transition process and are caused by fluctuations in the external E field due to EHD instabilities. The Ginzburg-Landau approach brings us back to the free energy functional F of the system [41][42][43][44]. Calculating the extrema with respect to Ψ yields the stationary, non-linear Ginzburg-Landau equation,…”

“…It is indeed non-vanishing while approaching the free energy minimum. As a result, the so-called time-dependent Ginzburg-Landau (TDGL) [41][42][43][44] equation is obtained…”

“…This second term vanishes when the stationary regime is reached. A more detailed discussion of Equation 13is given elsewhere [41][42][43][44], and reveals how the phase transition begins with an abrupt, adiabatic event, often called the null spike due to its extreme spatiotemporal localization. This singularity constitutes the core whence a vortex starts to form with the new phase emerging around the singularity.…”

“…Due to the non-linearity of Equation (13) strong local variations in condensate density will result. The vortex equation is indeed obtained from the TDGL Equation (13) (for the detailed derivation cf., e.g., [42,43]).…”