A space-time variational formulation for the many-body electronic Schr\"odinger evolution equation
<|reference_start|>A space-time variational formulation for the many-body electronic Schr\"odinger evolution equation: We prove in this paper that the solution of the time-dependent Schr{\"o}dinger equation can be expressed as the solution of a global space-time quadratic minimization problem that is amenable to Galerkin time-space discretization schemes, using an appropriate least-square formulation. The present analysis can be applied to the electronic many-body time-dependent Schr{\"o}dinger equation with an arbitrary number of electrons and interaction potentials with Coulomb singularities. We motivate the interest of the present approach with two goals: first, the design of Galerkin space-time discretization methods; second, the definition of dynamical low-rank approximations following a variational principle different from the classical Dirac-Frenkel principle, and for which it is possible to prove the global-in-time existence of solutions.<|reference_end|>
@article{dupuy2024a,
    title={A space-time variational formulation for the many-body electronic
  Schr{\"o}dinger evolution equation},
    author={Mi-Song Dupuy (LJLL (UMR_7598)), Virginie Ehrlacher (ENPC,
  MATHERIALS), Cl'ement Guillot (ENPC, MATHERIALS)},
    journal={arXiv preprint arXiv:2405.18094},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.18094},
    primaryClass={math.NA cs.NA}
}