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Bifurcation analysis for phase transitions in superconducting rings with nonuniform thickness. (English) Zbl 0911.35041

The authors analyze the different kinds of functions that minimize the thermodynamic potential in the Little-Parks experiment, which depend upon the temperature and the magnatic flux, with the deviation from uniform thickness as an additional parameter. They got the result that the “phase diagram” (the boundaries between qualitatively different minimizers in the temperature-flux plane) contains several bifurcation lines and critical points. They also provide an analytic treatment of the minimization problem near the bifurcation lines and the critical points.

MSC:

35J50 Variational methods for elliptic systems
82D55 Statistical mechanics of superconductors
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