New dynamical low-complexity approximations for the Schrödinger equation | Vidéo | Carmin.tv

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New dynamical low-complexity approximations for the Schrödinger equation

De Virginie Ehrlacher

Apparaît dans la collection : SIGMA (Signal, Image, Geometry, Modeling, Approximation) / SIGMA (Signal, Image, Géométrie, Modélisation, Approximation)

The aim of this talk is to present a new variation formulation of the time-dependent many-body electronic Schrödinger equation with Coulombic singularities. More precisely, its solution can actually be expressed as the solution of a global space-time quadratic minimization problem that proves to be useful for several tasks: 1) first, it is amenable to Galerkin time-space discretization schemes, using an appropriate least-square formulation 2) it enables to yield a new variational principle for the construction dynamical low-rank approximations, that is different from the classical Dirac-Frenkel variational principle 3) it enables to obtain fully certified a posteriori error estimators between the exact solution and approximate solutions. The present analysis can be applied to the electronic many-body time-dependent Schrödinger equation with an arbitrary number of electrons and interaction potentials with Coulomb singularities.

Informations sur la vidéo

Date de captation 29/10/2024
Date de publication 22/11/2024
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.20257803
Citer cette vidéo Ehrlacher, Virginie (29/10/2024). New dynamical low-complexity approximations for the Schrödinger equation. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20257803
URL https://dx.doi.org/10.24350/CIRM.V.20257803

Domaine(s)

Analyse numérique

Bibliographie

DUPUY, Mi-Song, EHRLACHER, Virginie, et GUILLOT, Clément. A space-time variational formulation for the many-body electronic Schrödinger evolution equation. arXiv preprint arXiv:2405.18094, 2024. - https://arxiv.org/abs/2405.18094

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