Speaker: Markus Penz
Title: Sobolev space formulation of density-functional theory: Solving the v-representability problem
Abstract: Density-functional theory is one of the principal methods in physics, chemistry, and materials science used for calculating properties of many-body systems based on their electronic structure. It rests on a reformulation of the explicit energy expression in terms of the full quantum state into an implicit energy functional defined for a reduced quantity, the one-particle density. While considerably reducing the computational complexity, if corresponding approximations are available, this reformulation introduces certain mathematical problems. Most notably, it is not explicitly known which set of densities actually stems from solutions to the quantum many-body problem, i.e., the lowest-eigenvalue solution to the time-independent Schrödinger equation. In this talk, a recently found resolution to this so-called "v-representability problem" is presented in the reduced setting of a 1-dim ring system with densities from a Sobolev space.