Convergence of Ginzburg-Landau functionals in 3-d superconductivity

作者: Giandomenico Orlandi , Sisto Baldo , R. Jerrard , H. M. Soner

DOI: 10.1007/S00205-012-0527-2

关键词:

摘要: In this paper we consider the asymptotic behavior of Ginzburg- Landau model for superconductivity in 3-d, various energy regimes. We rigorously derive, through an analysis via {\Gamma}-convergence, a reduced vortex density, and deduce curvature equation lines. companion paper, describe further applications to superfluidity, such as general expressions first critical magnetic field H_{c1}, angular velocity rotating Bose-Einstein condensates.

参考文章(32)
Etienne Sandier, Sylvia Serfaty, Vortices in the Magnetic Ginzburg-Landau Model ,(2008)
Robert L. Jerrard, Halil Mete Soner, The Jacobian and the Ginzburg-Landau energy Calculus of Variations and Partial Differential Equations. ,vol. 14, pp. 151- 191 ,(2002) , 10.1007/S005260100093
Herbert Federer, Geometric Measure Theory ,(1969)
L. Riekert, K. J. Laidler: Chemical Kinetics, Second Edition. Mc Graw Hill Book Company, New York 1965. 566 Seiten. Preis: $ 9,50 Berichte der Bunsengesellschaft für physikalische Chemie. ,vol. 70, pp. 392- 392 ,(1966) , 10.1002/BBPC.19660700316
T. Iwaniec, C. Scott, B. Stroffolini, Nonlinear Hodge theory on manifolds with boundary Annali di Matematica Pura ed Applicata. ,vol. 177, pp. 37- 115 ,(1999) , 10.1007/BF02505905
Robert Jerrard, Alberto Montero, Peter Sternberg, Local Minimizers of the Ginzburg-Landau Energy with Magnetic Field in Three Dimensions Communications in Mathematical Physics. ,vol. 249, pp. 549- 577 ,(2004) , 10.1007/S00220-004-1082-Y
DAVID CHIRON, BOUNDARY PROBLEMS FOR THE GINZBURG–LANDAU EQUATION Communications in Contemporary Mathematics. ,vol. 07, pp. 597- 648 ,(2005) , 10.1142/S0219199705001908
Sisto Baldo, Giandomenico Orlandi, A note on the Hodge theory for functionals with linear growth Manuscripta Mathematica. ,vol. 97, pp. 453- 467 ,(1998) , 10.1007/S002290050114
Giovanni Alberti, Sisto Baldo, Giandomenico Orlandi, Variational convergence for functionals of Ginzburg-Landau type. Indiana University Mathematics Journal. ,vol. 54, pp. 1411- 1472 ,(2005) , 10.1512/IUMJ.2005.54.2601
Etienne Sandier, Lower Bounds for the Energy of Unit Vector Fields and Applications Journal of Functional Analysis. ,vol. 152, pp. 379- 403 ,(1998) , 10.1006/JFAN.1997.3170