Time-dependent current density functional theory on a lattice
Time-dependent current density functional theory on a lattice
A rigorous formulation of time-dependent current density functional theory (TDCDFT) on a lattice is presented. The density-to-potential mapping and the $\mathcal{V}$-representability problems are reduced to a solution of a certain nonlinear lattice Schr\"odinger equation, to which the standard existence and uniqueness results for nonlinear differential equations are applicable. For two …