Threshold transition energies for Ginzburg-Landau functionals
Luís Almeida; Luís Almeida; Centre de Mathématiques et de Leurs Applications, Unité associée au CNRS URA-1611, Ecole Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235 Cachan Cedex, France
Журнал:
Nonlinearity
Дата:
1999-09-01
Аннотация:
In a previous paper (Almeida L 1996 Topological sectors for Ginzburg-Landau energies Rev. Mat. Iberoamericana to appear (preliminary version in author's thesis, ENS Cachan, January 1996)) we studied the components of level sets of Ginzburg-Landau energy functionals on multiply connected domains, and showed that they can be (partially) classified by an extended notion of topological degree. We used this to show the existence of stable states and mountain-pass solutions of Ginzburg-Landau equations. In this work, partly inspired by the techniques we developed with Bethuel (Almeida L and Bethuel F 1998 Topological methods for the Ginzburg-Landau equation J. Math. Pures Appl. 77 1-49), we first improve the classification into topological sectors of our earlier mentioned paper, and then obtain quite precise estimates on the threshold transition energies between different sectors. These enable us to, in the setting of the simple models considered, obtain the existence of states whose condensed wavefunction has a non-vanishing topological degree and which are separated from the ground state by very high-energy barriers - this phenomenon can be linked to the great stability of permanent currents in superconducting rings.
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