Schrödinger operator with magnetic field in domain with corners
- [1] IRMAR, Université Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France
Journées Équations aux dérivées partielles (2005)
- page 1-12
- ISSN: 0752-0360
Access Full Article
topAbstract
topHow to cite
topBonnaillie Noël, Virginie. "Schrödinger operator with magnetic field in domain with corners." Journées Équations aux dérivées partielles (2005): 1-12. <http://eudml.org/doc/10609>.
@article{BonnaillieNoël2005,
abstract = {We present here a simplified version of results obtained with F. Alouges, M. Dauge, B. Helffer and G. Vial (cf [4, 7, 9]). We analyze the Schrödinger operator with magnetic field in an infinite sector. This study allows to determine accurate approximation of the low-lying eigenpairs of the Schrödinger operator in domains with corners. We complete this analysis with numerical experiments.},
affiliation = {IRMAR, Université Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France},
author = {Bonnaillie Noël, Virginie},
journal = {Journées Équations aux dérivées partielles},
keywords = {Schrödinger operator; essential spectrum; domains with corners},
language = {eng},
month = {6},
pages = {1-12},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Schrödinger operator with magnetic field in domain with corners},
url = {http://eudml.org/doc/10609},
year = {2005},
}
TY - JOUR
AU - Bonnaillie Noël, Virginie
TI - Schrödinger operator with magnetic field in domain with corners
JO - Journées Équations aux dérivées partielles
DA - 2005/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 12
AB - We present here a simplified version of results obtained with F. Alouges, M. Dauge, B. Helffer and G. Vial (cf [4, 7, 9]). We analyze the Schrödinger operator with magnetic field in an infinite sector. This study allows to determine accurate approximation of the low-lying eigenpairs of the Schrödinger operator in domains with corners. We complete this analysis with numerical experiments.
LA - eng
KW - Schrödinger operator; essential spectrum; domains with corners
UR - http://eudml.org/doc/10609
ER -
References
top- Agmon, S.Lectures on exponential decay of solutions of second-order elliptic equations: bounds on eigenfunctions of -body Schrödinger operators, vol. 29 of Mathematical Notes. Princeton University Press, Princeton, NJ, 1982. Zbl0503.35001MR745286
- Alouges, F., and Bonnaillie, V. Analyse numérique de la supraconductivité. C. R. Math. Acad. Sci. Paris 337, 8 (2003), 543–548. Zbl1035.65121MR2017694
- Bernoff, A., and Sternberg, P. Onset of superconductivity in decreasing fields for general domains. J. Math. Phys. 39, 3 (1998), 1272–1284. Zbl1056.82523MR1608449
- Bonnaillie, V.Analyse mathématique de la supraconductivité dans un domaine à coins; méthodes semi-classiques et numériques. Thèse de doctorat, Université Paris XI - Orsay, 2003.
- Bonnaillie, V. On the fundamental state for a Schrödinger operator with magnetic field in a domain with corners. C. R. Math. Acad. Sci. Paris 336, 2 (2003), 135–140. Zbl1038.35043MR1969567
- Bonnaillie, V. Superconductivity in general domains. Prépublications d’Orsay 2004-09, 2004.
- Bonnaillie, V. On the fundamental state energy for a Schrödinger operator with magnetic field in domains with corners. Asymptot. Anal. 41, 3-4 (2005), 215–258. Zbl1067.35054MR2127997
- Bonnaillie Noël, V. A posteriori error estimator for the eigenvalue problem associated to the Schrödinger operator with magnetic field. Numer. Math. 99, 2 (2004), 325–348. Zbl1061.65114MR2107434
- Bonnaillie Noël, V., and Dauge, M. Asymptotics for the low-lying eigenstates of the Schrödinger operator with magnetic field near corner. In preparation, 2005. Zbl1134.81021MR2254755
- Cycon, H. L., Froese, R. G., Kirsch, W., and Simon, B.Schrödinger operators with application to quantum mechanics and global geometry, study ed. Texts and Monographs in Physics. Springer-Verlag, Berlin, 1987. Zbl0619.47005MR883643
- Dauge, M., and Helffer, B. Eigenvalues variation. I. Neumann problem for Sturm-Liouville operators. J. Differential Equations 104, 2 (1993), 243–262. Zbl0784.34021MR1231468
- Fournais, S., and Helffer, B. Accurate eigenvalue estimates for the magnetic neumann laplacian. To appear in Annales Inst. Fourier (2005). Zbl1097.47020
- Ginzburg, V., and Landau, L. On the theory of the superconductivity. Soviet. Phys. JETP 20 (1950), 1064–1082.
- Helffer, B.Semi-classical analysis for the Schrödinger operator and applications, vol. 1336 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1988. Zbl0647.35002MR960278
- Helffer, B., and Mohamed, A. Semiclassical analysis for the ground state energy of a Schrödinger operator with magnetic wells. J. Funct. Anal. 138, 1 (1996), 40–81. Zbl0851.58046MR1391630
- Helffer, B., and Morame, A. Magnetic bottles in connection with superconductivity. J. Funct. Anal. 185, 2 (2001), 604–680. Zbl1078.81023MR1856278
- Helffer, B., and Sjöstrand, J. Multiple wells in the semiclassical limit. I. Comm. Partial Differential Equations 9, 4 (1984), 337–408. Zbl0546.35053MR740094
- Jadallah, H. T. The onset of superconductivity in a domain with a corner. J. Math. Phys. 42, 9 (2001), 4101–4121. Zbl1063.82041MR1852538
- Lu, K., and Pan, X.-B. Estimates of the upper critical field for the Ginzburg-Landau equations of superconductivity. Phys. D 127, 1-2 (1999), 73–104. Zbl0934.35174MR1678383
- Lu, K., and Pan, X.-B. Gauge invariant eigenvalue problems in and in . Trans. Amer. Math. Soc. 352, 3 (2000), 1247–1276. Zbl1053.35124MR1675206
- Martin, D. http://perso.univ-rennes1.fr/daniel.martin/melina.
- Pan, X.-B. Upper critical field for superconductors with edges and corners. Calc. Var. Partial Differential Equations 14, 4 (2002), 447–482. Zbl1006.35090MR1911825
- Persson, A. Bounds for the discrete part of the spectrum of a semi-bounded Schrödinger operator. Math. Scand. 8 (1960), 143–153. Zbl0145.14901MR133586
- Simon, B. Semiclassical analysis of low lying eigenvalues. I. Nondegenerate minima: asymptotic expansions. Ann. Inst. H. Poincaré Sect. A (N.S.) 38, 3 (1983), 295–308. Zbl0526.35027MR708966
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.