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.

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