The Ground State Energy of the Three Dimensional Ginzburg-Landau Functional Part I: Bulk Regime |
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Authors: | Søren Fournais Ayman Kachmar |
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Institution: | 1. Department of Mathematical Sciences , University of Aarhus , ?rhus , Denmark fournais@imf.au.dk;3. Department of Mathematics , Lebanese University , Hadath , Lebanon;4. School of Arts and Sciences , Lebanese International University , Beirut , Lebanon |
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Abstract: | We consider the Ginzburg-Landau functional defined over a bounded and smooth three dimensional domain. Supposing that the magnetic field is comparable with the second critical field and that the Ginzburg-Landau parameter is large, we determine a precise asymptotic formula for the minimizing energy. In particular, this shows how bulk superconductivity decreases in average as the applied magnetic field approaches the second critical field from below. Other estimates are also obtained which allow us to obtain, in a subsequent paper 19
Fournais , S. ,
Kachmar , A. ,
Persson , M. The ground state energy of the three dimensional Ginzburg-Landau functional. Part II: Surface regime. Preprint. Google Scholar]], a fine characterization of the second critical field. The approach relies on a careful analysis of several limiting energies, which is of independent interest. |
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Keywords: | Elliptic estimates Ginzburg-Landau functional Magnetic Schrödinger operators Semiclassical analysis Thermodynamic limits Variational methods |
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