# Magnetic Schrödinger Operator: Geometry, Classical and Quantum Dynamics and Spectral Asymptotics

Séminaire Équations aux dérivées partielles (2006-2007)

- Volume: 2006-2007, page 1-23

## Access Full Article

top## Abstract

top## How to cite

topIvrii, Victor. "Magnetic Schrödinger Operator: Geometry, Classical and Quantum Dynamics and Spectral Asymptotics." Séminaire Équations aux dérivées partielles 2006-2007 (2006-2007): 1-23. <http://eudml.org/doc/11151>.

@article{Ivrii2006-2007,

abstract = {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.},

author = {Ivrii, Victor},

journal = {Séminaire Équations aux dérivées partielles},

keywords = {magnetic Schrödinger operator; magnetic field; dynamics; spectral asymptotic},

language = {eng},

pages = {1-23},

publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},

title = {Magnetic Schrödinger Operator: Geometry, Classical and Quantum Dynamics and Spectral Asymptotics},

url = {http://eudml.org/doc/11151},

volume = {2006-2007},

year = {2006-2007},

}

TY - JOUR

AU - Ivrii, Victor

TI - Magnetic Schrödinger Operator: Geometry, Classical and Quantum Dynamics and Spectral Asymptotics

JO - Séminaire Équations aux dérivées partielles

PY - 2006-2007

PB - Centre de mathématiques Laurent Schwartz, École polytechnique

VL - 2006-2007

SP - 1

EP - 23

AB - 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.

LA - eng

KW - magnetic Schrödinger operator; magnetic field; dynamics; spectral asymptotic

UR - http://eudml.org/doc/11151

ER -

## References

top- V. Ivrii. Microlocal Analysis and Precise Spectral Asymptotics, Springer-Verlag, SMM, 1998, xv+731. Zbl0906.35003MR1631419
- V. Ivrii. Sharp spectral asymptotics for operators with irregular coefficients. III. Schrödinger operator with a strong magnetic field, 81pp (to appear). Zbl1186.35204MR1807155
- 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). MR1807155
- 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). MR1807155
- V. Ivrii. Sharp spectral asymptotics for two-dimensional Schrödinger operator with a strong degenerating magnetic field., 79pp (to appear). Zbl1186.35204MR1006532
- V. Ivrii. Sharp spectral Asymptotics for 2-dimensional Schrödinger operator with a strong but degenerating magnetic field. II, 31pp (to appear).
- V. Ivrii. Sharp spectral asymptotics for 2-dimensional Schrödinger operator with a strong magnetic field. Note about forgotten generic case, 6pp (to appear).
- V. Ivrii. Sharp spectral asymptotics for four-dimensional Schrödinger operator with a strong degenerating magnetic field., 93pp (to appear).
- V. Ivrii. Sharp spectral asymptotics for generic 4-dimensional Schrödinger operator with the strong magnetic field, $\approx $60pp (in progress). Zbl1186.35204
- J. Martinet, Sur les singularites des formes differentielles, Ann. Inst. Fourier, 20 (1970), 1, 95-178. Zbl0189.10001MR286119
- R. Roussarie. Modèles locaux de champs et de forms Astérisque, 30 (1975) 3–179. Zbl0327.57017MR440570

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.