The resistive state in a superconducting wire: Bifurcation from the normal state

Archive for Rational Mechanics and Analysis

Volumn 195, Issue 1, 2009, Pages 117-158

  Rubinstein, Jacob ^a   Sternberg, Peter ^a   Zumbrun, Kevin ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70350637467     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-008-0188-3     Document Type: Article

References (20)

1. Almog, Y.: The stability of the normal state of superconductors in the presence of electric currents. preprint, 2007.
2. Bender C.M., Boettcher S.: Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80, 5243 (1998).
3. Bressan, A.: A tutorial on the center manifold theorem. Appendix A, Hyperbolic Systems of Balance Laws. Lecture Notes in Mathematics, vol. 1911. Springer, Berlin, 2007.
4. Caliceti E., Graffi S., Sjöstrand J.: Spectra of PT-symmetric operators and perturbation theory. J. Phys. A. 38, 185-193 (2005).
5. Cannata F., Dedonder J.-P., Ventura A.: Scattering in PT-symmetric quantum mechanics. Ann. Phys. 322(2), 397-433 (2007).
6. Hale J., Kocak H.: Dynamics and Bifurcations. Springer, Berlin (1991).
7. Henry D.: Geometric theory of semilinear parabolic equations. Lecture Notes in Mathematics, vol. 840. Springer, Berlin (1981).
8. Ivlev B.I., Kopnin N.B.: Electric currents and resistive states in thin superconductors. Adv. Phys. 33, 47-114 (1984).
9. Kramer L., Baratoff A.: Lossless and dissipative current carrying states in quasi one-dimensional superconductors. Phys. Rev. Lett. 38(9), 518-521 (1977).
10. Kramer L., Watts-Tobin R.J.: Theory of dissipative current carrying states in superconducting filaments. Phys. Rev. Lett. 40, 1041 (1978).
11. Langer J.E., Ambegaokar V.: Intrinsic resistive transition in narrow superconducting channels. Phys. Rev. 164, 498 (1967).
12. Langer H., Tretter C.: A Krein space approach to PT-symmetry. Czecoslovak J. Phys. 54, 1113-1120 (2004).
13. Ma T., Wang S.: Bifurcation Theory and Applications. World Scientific, Singapore (2005).
14. Rubinstein J., Sternberg P., Ma Q.: Bifurcation diagram and pattern formation in superconducting wires with electric currents. Phys. Rev. Lett. 99, 167003 (2007).
15. Rubinstein, J., Sternberg, P., Zumbrun, K.: Resistive state in a superconducting wire: Bifurcation from the normal state. (unabridged version with more details), arXiv:0712.3531.
16. Shkalikov A.A.: The limit behavior of the spectrum for large parameter value in a model problem. Math. Notes 62, 796-799 (1997).
17. Shkalikov A.A.: Spectral portraits of the Orr-Sommerfeld operator with large Reynolds numbers. J. Math. Sci. 124, 5417-5441 (2004).
18. Texier B., Zumbrun K.: Relative Poincaré-Hopf bifurcation and galloping instability of traveling waves. Meth. Appl. Anal. 12(4), 349-380 (2005).
19. Tinkham M.: Introduction to Superconductivity. McGraw-Hill, New York (1996).
20. Vodolazov D.V., Peeters F.M., Piraux L., Matten-Tempfli S., Michotte S.: Current-voltage characteristics of quasi one dimensional superconductors: An s-shaped curve in the constant voltage regime. Phys. Rev. Lett. 91, 157001 (2003).