Appears in collection : SIGMA (Signal, Image, Geometry, Modeling, Approximation) / SIGMA (Signal, Image, Géométrie, Modélisation, Approximation)
The aim of this talk is to present a new variation formulation of the time-dependent many-body electronic Schrödinger equation with Coulombic singularities. More precisely, its solution can actually be expressed as the solution of a global space-time quadratic minimization problem that proves to be useful for several tasks: 1) first, it is amenable to Galerkin time-space discretization schemes, using an appropriate least-square formulation 2) it enables to yield a new variational principle for the construction dynamical low-rank approximations, that is different from the classical Dirac-Frenkel variational principle 3) it enables to obtain fully certified a posteriori error estimators between the exact solution and approximate solutions. 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.
By Philipp Petersen
By Maria-Lucia Sampoli
