A variational problem concerning the "first" eigenvalue of a Dirac operator

par Matthieu Lewin (Ceremade, Université Paris-Dauphine, CNRS)

lundi 27 mars 2023, 11:00 → 12:00 Europe/Paris

I will discuss a conjecture concerning the minimization of the lowest positive eigenvalue of a family of Dirac operator, with respect to the external potential. This describes one quantum relativistic electron in the field of several nuclei and the question is to determine the nuclear charge distribution giving the lowest possible eigenvalue. This problem is well known and relatively easy for the Laplacian. It turned out to be very difficult for Dirac, where it is still largely open. Joint work with Maria J. Esteban and Eric Séré (Dauphine).