Dynamics of the Ginzburg-Landau equations of superconductivity
- Universite Toulouse (France)
- Argonne National Lab., IL (United States)
- Universitaet Rostock (Germany). Fachbereich Mathematik
This article is concerned with the dynamical properties of solutions of the time-dependent Ginzburg-Landau (TDGL) equations of superconductivity. It is shown that the TDGL equations define a dynamical process when the applied magnetic field varies with time, and a dynamical system when the applied magnetic field is stationary. The dynamical system describes the large-time asymptotic behavior: Every solution of the TDGL equations is attracted to a set of stationary solutions, which are divergence free. These results are obtained in the {open_quotes}{phi} = -{omega}({gradient}{center_dot}A){close_quotes} gauge, which reduces to the standard {close_quotes}{phi} = -{gradient}{center_dot}A{close_quotes} gauge if {omega} = 1 and to the zero-electric potential gauge if {omega} = 0; the treatment captures both in a unified framework. This gauge forces the London gauge, {gradient}{center_dot}A = 0, for any stationary solution of the TDGL equations.
- Research Organization:
- Argonne National Lab., IL (United States)
- Sponsoring Organization:
- USDOE Office of Energy Research, Washington, DC (United States); Commission of the European Communities, Brussels (Belgium); National Science Foundation, Washington, DC (United States)
- DOE Contract Number:
- W-31109-ENG-38
- OSTI ID:
- 516027
- Report Number(s):
- ANL/MCS/PP--89260; ON: DE97008270; CNN: European Community Contract ERBCHRXCT930409; NSF Grant DMS-9401418
- Country of Publication:
- United States
- Language:
- English
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