I study the Schrödinger operator with the strong magnetic field, considering links between geometry of magnetic field, classical and quantum dynamics associated with operator and spectral asymptotics. In particular, I will discuss the role of short periodic trajectories.
@article{SEDP_2006-2007____A16_0, author = {Ivrii, Victor}, title = {Magnetic {Schr\"odinger} {Operator:} {Geometry,} {Classical} and {Quantum} {Dynamics} and {Spectral} {Asymptotics}}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:16}, pages = {1--23}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2006-2007}, language = {en}, url = {http://www.numdam.org/item/SEDP_2006-2007____A16_0/} }
TY - JOUR AU - Ivrii, Victor TI - Magnetic Schrödinger Operator: Geometry, Classical and Quantum Dynamics and Spectral Asymptotics JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:16 PY - 2006-2007 SP - 1 EP - 23 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/item/SEDP_2006-2007____A16_0/ LA - en ID - SEDP_2006-2007____A16_0 ER -
%0 Journal Article %A Ivrii, Victor %T Magnetic Schrödinger Operator: Geometry, Classical and Quantum Dynamics and Spectral Asymptotics %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:16 %D 2006-2007 %P 1-23 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/item/SEDP_2006-2007____A16_0/ %G en %F SEDP_2006-2007____A16_0
Ivrii, Victor. Magnetic Schrödinger Operator: Geometry, Classical and Quantum Dynamics and Spectral Asymptotics. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2006-2007), Exposé no. 16, 23 p. http://www.numdam.org/item/SEDP_2006-2007____A16_0/
[Ivr1] V. Ivrii. Microlocal Analysis and Precise Spectral Asymptotics, Springer-Verlag, SMM, 1998, xv+731. | MR | Zbl
[Ivr2] V. Ivrii. Sharp spectral asymptotics for operators with irregular coefficients. III. Schrödinger operator with a strong magnetic field, 81pp (to appear). | MR
[Ivr3] V. Ivrii. Sharp spectral asymptotics for operators with irregular coefficients. IV. Multidimensional Schrödinger operator with a strong magnetic field. Full-rank case, 83pp (to appear). | MR
[Ivr4] V. Ivrii. Sharp spectral asymptotics for operators with irregular coefficients. V. Multidimensional Schrödinger operator with a strong magnetic field. Non-full-rank case, 78pp (to appear). | MR
[Ivr5] V. Ivrii. Sharp spectral asymptotics for two-dimensional Schrödinger operator with a strong degenerating magnetic field., 79pp (to appear). | MR
[Ivr6] V. Ivrii. Sharp spectral Asymptotics for 2-dimensional Schrödinger operator with a strong but degenerating magnetic field. II, 31pp (to appear).
[Ivr7] V. Ivrii. Sharp spectral asymptotics for 2-dimensional Schrödinger operator with a strong magnetic field. Note about forgotten generic case, 6pp (to appear).
[Ivr8] V. Ivrii. Sharp spectral asymptotics for four-dimensional Schrödinger operator with a strong degenerating magnetic field., 93pp (to appear).
[Ivr9] V. Ivrii. Sharp spectral asymptotics for generic 4-dimensional Schrödinger operator with the strong magnetic field, 60pp (in progress).
[Ma] J. Martinet, Sur les singularites des formes differentielles, Ann. Inst. Fourier, 20 (1970), 1, 95-178. | Numdam | MR | Zbl
[Rou] R. Roussarie. Modèles locaux de champs et de forms Astérisque, 30 (1975) 3–179. | Numdam | MR | Zbl