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Regularity of many-body Schrödinger evolution equation and its application to numerical analysis

Meng, Long (2019-05), Regularity of many-body Schrödinger evolution equation and its application to numerical analysis. https://basepub.dauphine.fr/handle/123456789/19410

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02129838
Date
2019-05
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
29
Metadata
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Author(s)
Meng, Long
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
A decade ago, the mixed regularity of stationary many-body Schr\"o\-dinger equation has been studied by Harry Yserentant through the Pauli Principle and the Hardy inequality (Uncertainty Principle). In this article, we prove that the many-body evolution Schr\"odinger equation has a similar mixed regularity if the initial data u0 satisfies the Pauli Principle. By generalization of the Strichartz estimates, our method also applies to the numerical approximation of this problem: based on these mixed derivatives, we design a new approximation which can hugely improve the computing capability especially in quantum chemistry.
Subjects / Keywords
many-body Schrödinger evolution equation