@article{ASENS_1989_4_22_4_515_0, author = {Helffer, B. and Nourrigat, J. and Wang, X. P.}, title = {Sur le spectre de l{\textquoteright}\'equation de {Dirac} (dans $\mathbb {R}^3$ ou $\mathbb {R}^2$) avec champ magn\'etique}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {515--533}, publisher = {Elsevier}, volume = {4e s{\'e}rie, 22}, number = {4}, year = {1989}, doi = {10.24033/asens.1591}, mrnumber = {91e:35155}, zbl = {0703.35127}, language = {fr}, url = {https://www.numdam.org/articles/10.24033/asens.1591/} }
TY - JOUR AU - Helffer, B. AU - Nourrigat, J. AU - Wang, X. P. TI - Sur le spectre de l’équation de Dirac (dans $\mathbb {R}^3$ ou $\mathbb {R}^2$) avec champ magnétique JO - Annales scientifiques de l'École Normale Supérieure PY - 1989 SP - 515 EP - 533 VL - 22 IS - 4 PB - Elsevier UR - https://www.numdam.org/articles/10.24033/asens.1591/ DO - 10.24033/asens.1591 LA - fr ID - ASENS_1989_4_22_4_515_0 ER -
%0 Journal Article %A Helffer, B. %A Nourrigat, J. %A Wang, X. P. %T Sur le spectre de l’équation de Dirac (dans $\mathbb {R}^3$ ou $\mathbb {R}^2$) avec champ magnétique %J Annales scientifiques de l'École Normale Supérieure %D 1989 %P 515-533 %V 22 %N 4 %I Elsevier %U https://www.numdam.org/articles/10.24033/asens.1591/ %R 10.24033/asens.1591 %G fr %F ASENS_1989_4_22_4_515_0
Helffer, B.; Nourrigat, J.; Wang, X. P. Sur le spectre de l’équation de Dirac (dans $\mathbb {R}^3$ ou $\mathbb {R}^2$) avec champ magnétique. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 22 (1989) no. 4, pp. 515-533. doi : 10.24033/asens.1591. https://www.numdam.org/articles/10.24033/asens.1591/
[AH-CA] Ground State of a Spin 1/2 Charged Particle in a Two Dimensional Magnetic Field. (Physical review, A vol. 19, n° 6, June 1979, p. 2461-2462). | MR
et ,[AV-HE-SI] Schrödinger Operators with Magnetic Fields I General Interactions (Duke Math. Journal, vol. 45, 1978, p. 847-884). | MR | Zbl
, et ,[AV-SE] Paramagnetism for Non-Relativistic Electrons and Euclidean Massless Dirac Particles (Phys. Rev. Letters, vol. 42, n° 15, 9 April 1979).
et ,[BE-GE] On the Point Spectrum for Dirac Operators (Journal of Functional Analysis, vol. 71, 1987, p. 309-338). | MR | Zbl
et ,[C-F-K-S] Schrödinger Operators with Applications to Quantum Mechanics and Global Geometry, Texts and monographs in Physics, Springer Verlag. | Zbl
, , et ,[DUF] Un exemple de champ magnétique dans Rn (Duke Math. Journal, vol. 53, (3), 1983, p. 729-734). | MR | Zbl
,[FRO-LI-LO] Stability of Coulomb Systems with Magnetic Fields I the One-Electron Atom (Comm. Math. Phys., vol. 104, 1986, p. 251-270). | MR | Zbl
, et ,[GA-LA] Fonctions holomorphes et particule chargée dans un champ magnétique constant (Sem. P. Lelong, H. Skoda, Springer Lecture Notes, 1980-1981). | Zbl
et ,[HE-MO] Sur le spectre essentiel des opérateurs de Schrödinger avec champ magnétique (Ann. Institut Fourier, t. 38, 1988, fasc. 2, p. 95-113). | Numdam | MR | Zbl
et ,[HE-NO] Hypoellipticité maximale pour des opérateurs polynômes de champ de vecteur (Progress in Mathematics, Birkhauser, vol. 58). | MR | Zbl
et ,[IWA] The Essential Spectrum of two Dimensional Schrödinger Operators with Perturbed Magnetic Fields (J. Math. Kyoto Univ., vol. 23, (3), 1983, p. 475-480). (2) Magnetic Schrödinger Operators with Compact Resolvent (J. Math. Kyoto Univ., vol. 26, (3), 1986, p. 357-374). | Zbl
, (1)[KL] On the Point Spectrum of Dirac Operators (Helv. Phys. Acta, vol. 53, 1980, p. 453-462). | MR
,[KUR] On the Essential Spectrum of Schrödinger Operators with Vector Potentials (Sc. Papers Coll. Gen. Ed. University Tokyo, 23, 1973, p. 87-91). | MR | Zbl
,[LA-LI] Mécanique quantique, Théorie non-relativiste. | Zbl
et ,[LAV] Spectre d'opérateurs sur certaines variétés de Cauchy-Riemann et champ magnétique (Ann. Univ. Ferrara, Sez VII-Sc. Math., vol. 28, 1982, p. 31-37). (2) Changement de jauge de deuxième espèce pour l'équation de Landau et équations de Cauchy-Riemann tangentielle (C. R. Acad. Sci. Paris, t. 291, série A, 1980, p. 435-437). | MR | Zbl
, (1)[LE] Gauge Invariance of Schrödinger Operators and Related Spectral Properties (J. Op. Theory, 1983, p. 163-179). | MR | Zbl
,[LI-LO] Stability of Coulomb Systems with Magnetic Fields II the Many-Electron Atom and the One Electron Molecule (Comm. Math. Phys., vol. 104, 1986, p. 271-282). | MR | Zbl
et ,[LO-YA] Stability of Coulomb Systems with Magnetic Fields III Zero Energy Bound States of the Pauli Operator (Comm. Math. Phys., vol. 104, 1986, p. 283-290). | MR | Zbl
et ,[MO] Quelques remarques sur le spectre de l'opérateur de Schrödinger avec un champ magnétique [Comm. in P.D.E., 1989 (à paraître)].
,[RE-SI] Methods of Modern Mathematical Physics, Academic press. | Zbl
et ,[RO] Autour de l'approximation semi-classique. Progress in mathematics, Birkhauser, 1986. | Zbl
,[WA] Puits multiples pour l'opérateur de Dirac (Annales de l'I.H.P. section physique théorique, vol. 43, n° 3, 1985, p. 269-319). | Numdam | MR | Zbl
,- Confinement–deconfinement transitions for two-dimensional Dirac particles, Journal of Functional Analysis, Volume 266 (2014) no. 4, p. 2225 | DOI:10.1016/j.jfa.2013.07.018
- Résonances près de seuils d'opérateurs magnétiques de Pauli et de Dirac, Canadian Journal of Mathematics, Volume 65 (2013) no. 5, p. 1095 | DOI:10.4153/cjm-2012-057-7
- Maximal inequalities and Riesz transform estimates on L p spaces for magnetic Schrödinger operators II, Mathematische Zeitschrift, Volume 274 (2013) no. 1-2, p. 85 | DOI:10.1007/s00209-012-1059-z
- EIGENFUNCTIONS AT THE THRESHOLD ENERGIES OF MAGNETIC DIRAC OPERATORS, Reviews in Mathematical Physics, Volume 23 (2011) no. 02, p. 155 | DOI:10.1142/s0129055x11004254
- Maximal inequalities and Riesz transform estimates on Lp spaces for magnetic Schrödinger operators I, Journal of Functional Analysis, Volume 259 (2010) no. 7, p. 1631 | DOI:10.1016/j.jfa.2009.09.003
- Two-parameter asymptotics in magnetic Weyl calculus, Journal of Mathematical Physics, Volume 51 (2010) no. 12 | DOI:10.1063/1.3499660
- Scaling of the ground-state energy of relativistic ions in high locally bounded magnetic fields, Journal of Mathematical Physics, Volume 51 (2010) no. 8 | DOI:10.1063/1.3467037
- SPECTRAL THEORY OF NO-PAIR HAMILTONIANS, Reviews in Mathematical Physics, Volume 22 (2010) no. 01, p. 1 | DOI:10.1142/s0129055x10003874
- Compactness of the solution operator to ∂¯ in weighted L2-spaces, Journal of Functional Analysis, Volume 243 (2007) no. 2, p. 679 | DOI:10.1016/j.jfa.2006.09.004
- On the spectrum of magnetic Dirac operators with Coulomb-type perturbations, Journal of Functional Analysis, Volume 250 (2007) no. 2, p. 625 | DOI:10.1016/j.jfa.2007.04.016
- The single-particle pseudorelativistic Jansen–Hess operator with magnetic field, Journal of Physics A: Mathematical and General, Volume 39 (2006) no. 23, p. 7501 | DOI:10.1088/0305-4470/39/23/022
- Discreteness of Spectrum and Strict Positivity Criteria for Magnetic Schrödinger Operators, Communications in Partial Differential Equations, Volume 29 (2005) no. 3-4, p. 489 | DOI:10.1081/pde-120030406
- Schrödinger Operators with Singular Potentials, Stationary Partial Differential Equations, Volume 2 (2005), p. 407 | DOI:10.1016/s1874-5733(05)80014-2
- On perturbations of Dirac operators with variable magnetic field of constant direction, Journal of Mathematical Physics, Volume 45 (2004) no. 11, p. 4164 | DOI:10.1063/1.1792933
- Chapter 2 The dirac operator, Relativistic Electronic Structure Theory, Volume 11 (2002), p. 23 | DOI:10.1016/s1380-7323(02)80028-0
- Ground state of a spin-1/2 charged particle in a two-dimensional magnetic field, Journal of Mathematical Physics, Volume 42 (2001) no. 8, p. 3334 | DOI:10.1063/1.1379312
- Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring–type estimate, Duke Mathematical Journal, Volume 96 (1999) no. 1 | DOI:10.1215/s0012-7094-99-09604-7
- Exponential decay of eigenfuctions of Hamiltonians with short range potential, Journal d'Analyse Mathématique, Volume 76 (1998) no. 1, p. 205 | DOI:10.1007/bf02786936
- Lieb-Thirring Inequalities for the Pauli Operator in Three Dimensions, Quasiclassical Methods, Volume 95 (1997), p. 155 | DOI:10.1007/978-1-4612-1940-8_9
- Essential spectrum of the Dirac Hamiltonian for a spin 1/2 neutral particle with an anomalous magnetic moment in an asymptotically constant magnetic field, Journal of Mathematical Physics, Volume 37 (1996) no. 3, p. 1234 | DOI:10.1063/1.531458
Cité par 20 documents. Sources : Crossref