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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