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Spectral asymptotics of the one-particle density matrix for the Coulombic multi-particle systems
Multi angle
Authors : Sobolev, Alexander (Author of the conference)
CIRM (Publisher )
35J10 - Schrödinger operator
47G10 - Integral operators, See also {45P05}
Additional resources :
https://www.cirm-math.fr/RepOrga/2985/Slides/A_Sobolev.pdf
CIRM (Publisher )
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Abstract :
One-particle density matrix is the key object in the quantum-mechanical approximation schemes. In this talk I will give a short survey of recent regularity results with emphasis on sharp bounds for the eigenfunctions, and show how these bounds lead to the asymptotic formula for the eigenvalues of the one-particle density matrix. The argument is based on the results of M. Birman and M. Solomyak on spectral asymptotics for pseudo-differential operators with matrix-valued symbols.
Keywords : multi-particle Schrödinger operator; one-particle density matrix; eigenvalues; spectral asymptotics
MSC Codes : Keywords : multi-particle Schrödinger operator; one-particle density matrix; eigenvalues; spectral asymptotics
35J10 - Schrödinger operator
47G10 - Integral operators, See also {45P05}
Additional resources :
https://www.cirm-math.fr/RepOrga/2985/Slides/A_Sobolev.pdf
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Information on the Video
Film maker : Récanzone, LucaLanguage : English Available date : 01/02/2024 Conference Date : 15/01/2024 Subseries : Research talks arXiv category : Mathematical Physics ; Spectral Theory Mathematical Area(s) : Analysis and its Applications ; PDE ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 00:44:18 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-01-15_sobolev.mp4 
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Information on the Event
Event Title : Spectral Analysis for Quantum Hamiltonians / Analyse Spectrale pour des Hamiltoniens QuantiquesEvent Organizers : Briet, Philippe ; Bruneau, Vincent ; Miranda, Pablo ; Taarabt, Amal Dates : 15/01/2024 - 19/01/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/2985.html
Citation Data
DOI : 10.24350/CIRM.V.20127203Cite this video as: Sobolev, Alexander (2024). Spectral asymptotics of the one-particle density matrix for the Coulombic multi-particle systems. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20127203 URI : http://dx.doi.org/10.24350/CIRM.V.20127203 |
See Also
- [Multi angle] Spectral analysis in sheared waveguides / Author of the conference Verri, Alessandra.
- [Multi angle] Boundary states of the magnetic Robin Laplacian / Author of the conference Raymond, Nicolas.
- [Multi angle] Georgi's game of twist / Author of the conference Krejcirik, David.
- [Multi angle] The Landau Hamiltonian with delta-potentials supported on curves / Author of the conference Behrndt, Jussi.
Bibliography
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