Spectral asymptotics of the one-particle density matrix for the Coulombic multi-particle systems | Vidéo | Carmin.tv

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Spectral asymptotics of the one-particle density matrix for the Coulombic multi-particle systems

By Alexander Sobolev

Appears in collection : Spectral Analysis for Quantum Hamiltonians / Analyse Spectrale pour des Hamiltoniens Quantiques

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.

Information about the video

Date of recording 15/01/2024
Date of publication 01/02/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20127203
Cite this video Sobolev, Alexander (15/01/2024). Spectral asymptotics of the one-particle density matrix for the Coulombic multi-particle systems. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20127203
URL https://dx.doi.org/10.24350/CIRM.V.20127203

Domain(s)

Bibliography

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MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/2985/Slides/A_Sobolev.pdf

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