Discrete electrodynamics: potentials and quantum electronics

A general mathematical framework for the computational modelling of electromagnetic fields interacting with arbitrary quantum-electronic systems is described. The discretisation of space and time are taken as fundamental to the model, and the quantum-electronic systems with which the fields interact are taken to be discretised at each spa-tial mesh point. Maxwell equations are formulated on the discrete space using exact potentials and discrete forms of Stokes ’ Theorem. The discrete potentials interact with the quantum-electronic systems through the minimal coupling scheme (potential-momentum or A · p coupling). The entire scheme is essentially a finite-difference time-domain Maxwell-Bloch system (FDTD-MB) for potentials, with discrete exterior calculus (DEC) as the fundamental mathe-matical language. 1