Fast Evaluation of Retarded Electromagnetic Potentials for Quantum Calculations

A fast evaluation of retarded electromagnetic potentials is presented for quantum calculations on a uniform Cartesian grid. The induced potentials are incorporated into the quantum Hamiltonian of the time-dependent density functional theory (TDDFT) in real space. Both Lorentz and Coulomb gauge-fixed Hamiltonians are implemented using a real-time propagation scheme. The efficiency of the resulting formalism and implementation enables the evaluation of retardation effects on long carbon chains.