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

00:00:00 / 00:00:00

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

De Alexander Sobolev

Apparaît dans la 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.

Informations sur la vidéo

Date de captation 15/01/2024
Date de publication 01/02/2024
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Luca Recanzone
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20127203
Citer cette vidéo 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

Domaine(s)

Bibliographie

БИРМАН, Михаил Шлемович et СОЛОМЯК, Михаил Захарович. Асимптотика спектра слабо полярных интегральных операторов. Известия Российской академии наук. Серия математическая, 1970, vol. 34, no 5, p. 1142-1158. - https://doi.org/10.1070/IM1970v004n05ABEH000948
BIRMAN, M. Sh et SOLOMYAK, M. Z. Asymptotic behavior of the spectrum of pseudodifferential operators with anisotropically homogeneous symbols. Vestnik Leningrad. Univ., 1977, vol. 13, no 3, p. 13-21.
BIRMAN, M. Sh et SOLOMYAK, Mikhail Zakharovich. The asymptotics of the spectrum of pseudo-differential operators with anisotropic-homogeneous symbols. II, 1979, vol. 13, no 3, p. 5-10.
BIRMAN, M. Sh. et SOLOMYAK, Mikhail Zakharovich. Spectral theory of self-adjoint operators in Hilbert space Mathematics and its Applications (Soviet Series), D.Reidel, 1987. Translated from the 1980 Russian original by S. Khrushchev and V. Peller.
CIOSLOWSKI, Jerzy. Off-diagonal derivative discontinuities in the reduced density matrices of electronic systems. The Journal of Chemical Physics, 2020, vol. 153, no 15. - https://doi.org/10.1063/5.0023955
CIOSLOWSKI, Jerzy et PRĄTNICKI, Filip. Universalities among natural orbitals and occupation numbers pertaining to ground states of two electrons in central potentials. The Journal of Chemical Physics, 2019, vol. 151, no 18. - https://doi.org/10.1063/1.5123669
CIOSLOWSKI, Jerzy et STRASBURGER, Krzysztof. Angular-momentum extrapolations to the complete basis set limit: Why and when they work. Journal of Chemical Theory and Computation, 2021, vol. 17, no 6, p. 3403-3413. - https://doi.org/10.1021/acs.jctc.1c00202
COLEMAN, Albert John et YUKALOV, Vyacheslav I. Reduced density matrices: Coulson's challenge. Springer Science & Business Media, 2000.
DAVIDSON, Ernest. Reduced density matrices in quantum chemistry. Academic Press, 1976.
FOURNAIS, Søren et SØRENSEN, Thomas Østergaard. Pointwise estimates on derivatives of Coulombic wave functions and their electron densities. arXiv preprint arXiv:1803.03495, 2018. - https://doi.org/10.48550/arXiv.1803.03495
FOURNAIS, Søren, HOFFMANN-OSTENHOF, Maria, HOFFMANN-OSTENHOF, Thomas, et al. Analytic structure of many-body Coulombic wave functions. Communications in Mathematical Physics, 2009, vol. 289, p. 291-310. - http://dx.doi.org/10.1007/s00220-008-0664-5
FRIESECKE, G. On the infinitude of non–zero eigenvalues of the single–electron density matrix for atoms and molecules. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2003, vol. 459, no 2029, p. 47-52. - https://doi.org/10.1098/rspa.2002.1027
HATTIG, Christof, KLOPPER, Wim, KOHN, Andreas, et al. Explicitly correlated electrons in molecules. Chemical reviews, 2012, vol. 112, no 1, p. 4-74. - https://doi.org/10.1021/cr200168z
HEARNSHAW, Peter et SOBOLEV, Alexander V. Analyticity of the one-particle density matrix. arXiv preprint arXiv:2006.11785, 2020. - https://doi.org/10.1007/s00023-021-01120-6
KATO, Tosio. On the eigenfunctions of many‐particle systems in quantum mechanics. Communications on Pure and Applied Mathematics, 1957, vol. 10, no 2, p. 151-177. - https://doi.org/10.1002/cpa.3160100201
LEWIN, Mathieu, LIEB, Elliott H., et SEIRINGER, Robert. Universal functionals in density functional theory. In : Density Functional Theory: Modeling, Mathematical Analysis, Computational Methods, and Applications. Cham : Springer International Publishing, 2022. p. 115-182. - http://dx.doi.org/10.1007/978-3-031-22340-2_3
LIEB, Elliott H. et SEIRINGER, Robert. The stability of matter in quantum mechanics. Cambridge university press, 2010.
SIMON, Barry. Methods of Modern Mathematical Physics: Fourier Analysis, Self-Adjointness. 1975.
SIMON, B. Exponential decay of quantum wave functions. Online notes - http://www.math.caltech.edu/simon/Selecta/ExponentialDecay.pdf
SIMON, B. Simon's online Selecta - http://www.math.caltech.edu/simon/selecta.html
SOBOLEV, Alexander V. Eigenvalue estimates for the one-particle density matrix. arXiv e-prints, 2020, p. arXiv: 2008.10935. - https://doi.org/10.48550/arXiv.2008.10935

Codes MSC

Document(s)

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

Dernières questions liées sur MathOverflow

Pour poser une question, votre compte Carmin.tv doit être connecté à mathoverflow

Poser une question sur MathOverflow

Copyright Carmin.tv 2024

Donner son avis