Vortex analysis of the periodic Ginzburg-Landau model

 Access to full text

 Full (PDF)

1. [1] Abrikosov A., On the magnetic properties of superconductors of the second type, Soviet Phys. JETP5 (1957) 1174-1182. 
2. [2] Aftalion A., Blanc X., Nier F., Lowest Landau level functional and Bargmann spaces for Bose–Einstein condensates, J. Funct. Anal.241 (2) (2006) 661-702. Zbl1118.82004MR2271933
3. [3] Aftalion A., Serfaty S., Lowest Landau level approach in superconductivity for the Abrikosov lattice close to $H_{c_2}$, Selecta Math. (N.S.)13 (2) (2007) 183-202. Zbl1138.82034MR2361092
4. [4] Alama S., Bronsard L., Sandier E., On the shape of interlayer vortices in the Lawrence–Doniach model, Trans. Amer. Math. Soc.360 (2008) 1-34. Zbl1132.35081MR2341992
5. [5] Almog Y., On the bifurcation and stability of periodic solutions of the Ginzburg–Landau equations in the plane, SIAM J. Appl. Math.61 (1) (2000) 149-171. Zbl0967.82013MR1776391
6. [6] Almog Y., Abrikosov lattices in finite domains, Commun. Math. Phys.262 (3) (2006) 677-702. Zbl1106.35089MR2202308
7. [7] H. Aydi, Doctoral Dissertation, Université Paris-XII, 2004. 
8. [8] Bethuel F., Brezis H., Hélein F., Ginzburg–Landau Vortices, Progress in Nonlinear Partial Differential Equations and Their Applications, vol. 13, Birkhäuser Boston, Boston, 1994. Zbl0802.35142MR1269538
9. [9] Bethuel F., Rivière T., Vortices for a variational problem related to superconductivity, Ann. Inst. H. Poincaré Anal. Non Linéaire12 (3) (1995) 243-303. Zbl0842.35119MR1340265
10. [10] Brandt E.H., The flux-line lattice in superconductors, Rep. Prog. Phys.58 (1995) 1465-1594. 
11. [11] Comte M., Mironescu P., The behavior of a Ginzburg–Landau minimizer near its zeroes, Calc. Var. Partial Differential Equations4 (4) (1996) 323-340. Zbl0869.35036MR1393268
12. [12] Doria M.M., Gubernatis J.E., Rainer D., Solving the Ginzburg–Landau equations by simulated annealing, Phys. Rev. B41 (1990) 6335-6340. 
13. [13] Du Q., Gunzburger M.D., Peterson J.S., Modeling and analysis of a periodic Ginzburg–Landau model for type-II superconductors, SIAM J. Appl. Math.53 (3) (1993) 689-717. Zbl0784.35107MR1218380
14. [14] Dutour M., Bifurcation vers l'état d'Abrikosov et diagramme de phase, Thèse Orsay. Available online at:, http://xxx.lanl.gov/abs/math-ph/9912011. 
15. [15] Jerrard R.L., Lower bounds for generalized Ginzburg–Landau functionals, SIAM J. Math. Anal.30 (4) (1999) 721-746. Zbl0928.35045MR1684723
16. [16] Jerrard R.L., Soner H.M., The Jacobian and the Ginzburg–Landau energy, Calc. Var. Partial Differential Equations14 (2) (2002) 151-191. Zbl1034.35025MR1890398
17. [17] Kleiner W.H., Roth L.M., Autler S.H., Bulk solution of Ginzburg–Landau equations for type II superconductors: Upper critical field region, Phys. Rev.133 (1964) A1226-A1227. Zbl0115.45605
18. [18] Lasher G., Series solution of the Ginzburg–Landau equations for the Abrikosov mixed state, Phys. Rev. 2140 (1965) A523-A528. MR187819
19. [19] Mironescu P., Les minimiseurs locaux pour l'équation de Ginzburg–Landau sont à symétrie radiale, C. R. Acad. Sci. Paris, Ser. I323 (6) (1996) 593-598. Zbl0858.35038MR1411048
20. [20] Odeh F., Existence and bifurcation theorems for the Ginzburg–Landau equations, J. Math. Phys.8 (1967) 2351-2356. 
21. [21] Sandier E., Serfaty S., On the energy of type-II superconductors in the mixed phase, Rev. Math. Phys.12 (9) (2000) 1219-1257. Zbl0964.49006MR1794239
22. [22] Sandier E., Serfaty S., Vortices in the Magnetic Ginzburg–Landau Model, Progress in Nonlinear Differential Equations and Their Applications, vol. 70, Birkhäuser Boston Inc., Boston, MA, 2007. Zbl1112.35002MR2279839
23. [23] E. Sandier, S. Serfaty, From the Ginzburg–Landau model to vortex lattice problems, in preparation. Zbl1252.35034
24. [24] Serfaty S., Local minimizers for the Ginzburg–Landau energy near critical magnetic field, part I, Comm. Contemp. Math.1 (2) (1999) 213-254, part II, 295–333. Zbl0964.49005MR1696100
25. [25] Tinkham M., Introduction to Superconductivity, second ed., McGraw–Hill, New York, 1996.