Stationary state computation for nonlinear Dirac operators

Abstract

This paper is devoted to an emerging research topic, which is the numerical computation of stationary states of a generic Dirac operator with nonlinear potential. We are more specifically interested in the numerical computation of chemical potentials and eigenenergies. In this goal, several approaches are explored namely Feit-Fleck's, Rayleigh-Ritz, and min-max methods for the computation of chemical potentials, and normalized gradient flow methods for the eigenenergy computation. Balance operators will be introduced to ensure the convergence of some of the proposed methods. Finally, some numerical experiments will be proposed in order to validate the presented methods.