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HAIT Journal of Science and Engineering Volume 1, Issue 1, pp. 23-40 © 2004 Holon Academic Institute of Technology | ||||||
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A result on the phase diagram of a Ginzburg-Landau problem
Mathieu Dutour
Laboratoire Interdisciplinaire de Géométrie | Ecole Normale Supérieure, 45 rue d'Ulm, 75005 Paris, France and Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel e-mail: dutour@liga.ens.fr Received 3 July 2003
| We study mathematically the Abrikosov [JETP Lett. 32, 1174 (1957)] modelization of superconductors, which use the Ginzburg-Landau phenomenological theory. We first prove the qualitative shape of the phase diagram, which is found in the physical literature (M. Tinkham, 1996; C. Kittel, 1996; D. Saint-James, G. Sarma, and E.J. Thomas, 1969; P.G. de Gennes, 1966). We then study in detail the special case, when the critical Ginzburg Landau parameter k is equal to 1/√2. This allows us to prove that the critical magnetic field Hc1(k) is strictly decreasing at k=1/√2. PACS: 01.30.Cc, 02.30.Jr, 74.25.Dw
___________________ | Presented at International Workshop Quantum Processes and Modern Electronics III Holon Academic Institute of Technology, Holon, Israel, 5-6 January 2003 |