Confining quantum particles with a purely magnetic field
Yves Colin de Verdière[1]; Françoise Truc[2]
- [1] Institut Fourier UMR 5582 CNRS-UJF BP 74 38402 Saint Martin d’Hères Cedex (France)
- [2] Unité mixte de recherche CNRS-UJF 5582 Institut Fourier BP 74, 38402-Saint Martin d’Hères Cedex (France)
Annales de l’institut Fourier (2010)
- Volume: 60, Issue: 7, page 2333-2356
- ISSN: 0373-0956
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top- Shmuel Agmon, Lectures on exponential decay of solutions of second-order elliptic equations: bounds on eigenfunctions of -body Schrödinger operators, 29 (1982), Princeton University Press, Princeton, NJ Zbl0503.35001MR745286
- Paul Alexandroff, Heinz Hopf, Topologie. Band I, (1972), Chelsea Publishing Co., Bronx, N. Y. Zbl0013.07904MR396210
- J. Avron, I. Herbst, B. Simon, Schrödinger operators with magnetic fields. I. General interactions, Duke Math. J. 45 (1978), 847-883 Zbl0399.35029MR518109
- Alexander Balinsky, Ari Laptev, Alexander V. Sobolev, Generalized Hardy inequality for the magnetic Dirichlet forms, J. Statist. Phys. 116 (2004), 507-521 Zbl1127.26015MR2083152
- Yves Colin de Verdière, L’asymptotique de Weyl pour les bouteilles magnétiques, Comm. Math. Phys. 105 (1986), 327-335 Zbl0612.35102MR849211
- H. L. Cycon, R. G. Froese, W. Kirsch, B. Simon, Schrödinger operators with application to quantum mechanics and global geometry, (1987), Springer-Verlag, Berlin Zbl0619.47005MR883643
- Alain Dufresnoy, Un exemple de champ magnétique dans , Duke Math. J. 50 (1983), 729-734 Zbl0532.35021MR714827
- Nelson Dunford, Jacob T. Schwartz, Linear operators. Part III: Spectral operators, (1971), Interscience Publishers [John Wiley & Sons, Inc.], New York-London-Sydney Zbl0635.47003MR412888
- László Erdős, Jan Philip Solovej, Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields. I. Nonasymptotic Lieb-Thirring-type estimate, Duke Math. J. 96 (1999), 127-173 Zbl1047.81022MR1663923
- László Erdős, Jan Philip Solovej, Magnetic Lieb-Thirring inequalities with optimal dependence on the field strength, J. Statist. Phys. 116 (2004), 475-506 Zbl1138.81017MR2083151
- László Erdős, Jan Philip Solovej, Uniform Lieb-Thirring inequality for the three-dimensional Pauli operator with a strong non-homogeneous magnetic field, Ann. Henri Poincaré 5 (2004), 671-741 Zbl1054.81016MR2090449
- Victor Guillemin, Alan Pollack, Differential topology, (1974), Prentice-Hall Inc., Englewood Cliffs, N.J. Zbl0361.57001MR348781
- Juha Heinonen, Lectures on Lipschitz analysis, 100 (2005), University of Jyväskylä, Jyväskylä Zbl1086.30003MR2177410
- Teruo Ikebe, Tosio Kato, Uniqueness of the self-adjoint extension of singular elliptic differential operators, Arch. Rational Mech. Anal. 9 (1962), 77-92 Zbl0103.31801MR142894
- H. Kalf, U.-W. Schmincke, J. Walter, R. Wüst, On the spectral theory of Schrödinger and Dirac operators with strongly singular potentials, Spectral theory and differential equations (Proc. Sympos., Dundee, 1974; dedicated to Konrad Jörgens) (1975), 182-226. Lecture Notes in Math., Vol. 448, Springer, Berlin Zbl0311.47021MR397192
- Bertram Kostant, Quantization and unitary representations. I. Prequantization, Lectures in modern analysis and applications, III (1970), 87-208. Lecture Notes in Math., Vol. 170, Springer, Berlin Zbl0223.53028MR294568
- Ruishi Kuwabara, On spectra of the Laplacian on vector bundles, J. Math. Tokushima Univ. 16 (1982), 1-23 Zbl0504.53039MR691445
- Ruishi Kuwabara, Spectrum of the Schrödinger operator on a line bundle over complex projective spaces, Tohoku Math. J. (2) 40 (1988), 199-211 Zbl0652.53044MR943819
- Charles B. Morrey, Multiple integrals in the calculus of variations, (1966), Springer-Verlag New York, Inc., New York Zbl0142.38701MR202511
- Gheorghe Nenciu, Irina Nenciu, On confining potentials and essential self-adjointness for Schrödinger operators on bounded domains in , Ann. Henri Poincaré 10 (2009), 377-394 Zbl1205.81088MR2511891
- Gheorghe Nenciu, Irina Nenciu, Remarks on essential self-adjointness for magnetic Schrödinger and Pauli operators on bounded domains in , (2010) Zbl1242.81083
- Hans Rademacher, Über partielle und totale differenzierbarkeit von Funktionen mehrerer Variabeln und über die Transformation der Doppelintegrale, Math. Ann. 79 (1919), 340-359 Zbl47.0243.01MR1511935
- Michael Reed, Barry Simon, Methods of modern mathematical physics. II. Fourier analysis, self-adjointness, (1975), Academic Press [Harcourt Brace Jovanovich Publishers], New York Zbl0242.46001MR493420
- Mikhail Shubin, Essential self-adjointness for semi-bounded magnetic Schrödinger operators on non-compact manifolds, J. Funct. Anal. 186 (2001), 92-116 Zbl0997.58021MR1863293
- I. M. Sigal, Geometric methods in the quantum many-body problem. Nonexistence of very negative ions, Comm. Math. Phys. 85 (1982), 309-324 Zbl0503.47041MR676004
- Barry Simon, Essential self-adjointness of Schrödinger operators with singular potentials, Arch. Rational Mech. Anal. 52 (1973), 44-48 Zbl0277.47007MR338548
- Barry Simon, Schrödinger operators with singular magnetic vector potentials, Math. Z. 131 (1973), 361-370 Zbl0277.47006MR322336
- Nabila Torki-Hamza, Stabilité des valeurs propres et champ magnétique sur une variété riemannienne et sur un graphe, (1989)
- Françoise Truc, Trajectoires bornées d’une particule soumise à un champ magnétique symétrique linéaire, Ann. Inst. H. Poincaré Phys. Théor. 64 (1996), 127-154 Zbl0862.70005MR1386214
- Françoise Truc, Semi-classical asymptotics for magnetic bottles, Asymptot. Anal. 15 (1997), 385-395 Zbl0902.35079MR1487718