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By Jorge Berger, Jacob Rubinstein

Monograph serving as a reference for graduate scholars and researchers in physics or arithmetic drawn to superconductivity. can pay designated cognizance to the 'zero set, the set of positions frequently referred to as the 'quantum vortices,' during which the order parameter vanishes. DLC: Superconductivity--Mathematics.

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Lett. 16, 1096 (1970) P. Bauman, D. Phillips, Q. Tang: Arch. Rat. Mech. Anal. 142, 1 (1998) J. Berger, J. Rubinstein: Phys. Rev. Lett. 75, 320 (1995) J. Berger, J. Rubinstein: Phys. Rev. B. 56, 5124 (1997) J. Berger, J. Rubinstein: Comm. Math. Phys. 202, 621 (1999) J. Berger, J. Rubinstein: “Continuous phase transitions in mesoscopic systems”, ZAMP, in press 22 Jacob Rubinstein 9. A. Bernoff, P. Sternberg: J. Math. Phys. 39, 1272 (1998) 10. F. Bethuel: Acta Math. 167, 153 (1991) 11. H. Brezis, Y.

I. Castro and A. L´ opez Fig. 17. a) Spectrum of eigenvalues for the square ladder. The Floquet index takes on the values (kπ/10) where k is integer. b) Spectrum of eigenvalues for the square lattice. In both cases the lower part corresponds to symmetric modes and the upper part to antisymmetric modes. 1. In both cases the flux goes up to 2 flux quanta per unit cell (see text). (Taken from Ref. ) It is possible to obtain an analytical expression for the N-S phase boundary taking the lower value µ0 corresponding to a given applied flux φe ; this condition gives us the q value characterizing the nucleation mode of the order parameter at the N-S transition, which we call q0 .

39, 1272 (1998) 10. F. Bethuel: Acta Math. 167, 153 (1991) 11. H. Brezis, Y. Li, P. Mironescu, L. Nirenberg: “Degree and Sobolev Spaces”, preprint. 12. O. Buisson, P. Gandit, R. Y. Wang B. Pannetier: Phys. Lett. 150, 36 (1990). 13. G. de Gennes: Superconductivity in metals and Alloys, Addison Wesley (1989). 14. Q. D. S. Peterson: SIAM Review 34, 54, (1992) 15. P. D. Parks: Phys. Rev. 176, 567 (1968) 16. B. Helffer, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, M. Owen: Comm. Math. Phys. 202, 629, (1999) 17.

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