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

Long Meng (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

A decade ago, the mixed regularity of stationary many-body Schrödinger 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 Schrödinger equation has a similar mixed regularity if the initial data u 0 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.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Analyse numérique [math.NA]

Long Meng. Regularity of many-body Schrödinger evolution equation and its application to numerical analysis. 2020. ⟨hal-02994993v1⟩