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Pré-Publication, Document De Travail Année : 2023

Mixed regularity of $N$-body Schr\"odinger evolution equation and corresponding hyperbolic cross space approximation

Résumé

In this paper, we give a mathematical analysis of a time-dependent $N$-body electronic system in molecular dynamics. We first prove a mixed regularity of the corresponding wavefunctions. Thanks to this mixed regularity, we rigorously justify a hyperbolic cross space approximation of the $N$-body electronic system. The complexity of this approximation is close to that of a two-electrons problem, thus breaking the curse of dimensionality.
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Dates et versions

hal-02994993 , version 1 (08-11-2020)
hal-02994993 , version 2 (20-10-2023)

Identifiants

  • HAL Id : hal-02994993 , version 2

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Long Meng. Mixed regularity of $N$-body Schr\"odinger evolution equation and corresponding hyperbolic cross space approximation. 2023. ⟨hal-02994993v2⟩
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