A Space-Time Variational Formulation for the Many-Body Electronic Schrödinger Evolution Equation
Mi-Song Dupuy, Virginie Ehrlacher, Clément Guillot
Source abstract
Abstract. We prove in this paper that the solution to the time-dependent Schrödinger 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 Schrödinger 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.
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