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Not Only Scalar Curvature Seminar

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Applications of NonCommutative Geometry to Gauge Theories, Field Theories, and Quantum Space-Time / Applications de la Géométrie Non Commutative aux Théories de Jauge, à la Théorie des Champs et aux Espaces-Temps Quantiques
5 videos

Applications of NonCommutative Geometry to Gauge Theories, Field Theories, and Quantum Space-Time / Applications de la Géométrie Non Commutative aux Théories de Jauge, à la Théorie des Champs et aux Espaces-Temps Quantiques

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SIGMA (Signal, Image, Geometry, Modeling, Approximation) / SIGMA (Signal, Image, Géométrie, Modélisation, Approximation)

Collection SIGMA (Signal, Image, Geometry, Modeling, Approximation) / SIGMA (Signal, Image, Géométrie, Modélisation, Approximation)

Organizer(s) Cohen, Albert ; Digne, Julie ; Fadili, Jalal ; Mula, Olga ; Nouy, Anthony
Date(s) 28/10/2024 - 01/11/2024
linked URL https://conferences.cirm-math.fr/3066.html
00:00:00 / 00:00:00
3 5

New dynamical low-complexity approximations for the Schrödinger equation

By Virginie Ehrlacher

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.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.20257803
  • Cite this video 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

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Bibliography

  • 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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