Macroscopic descriptions of non-linear electromagnetic interactions in many-electron systems

Reduced-density-matrix descriptions are developed for linear and non-linear (possibly coherent) electromagnetic interactions of many-electron systems. Applications of interest include pump-probe optical phenomena in warm atomic vapors, partially-ionized plasmas, and condensed matter. Collision processes are treated within the framework of environmental perturbations, giving rise to decoherence and relaxation phenomena, and externally applied magnetic fields are taken into account on an equal footing with the electromagnetic fields. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified manner. The standard Born (lowest-order-perturbation) and Markov (short-memory-time) approximations are systematically introduced within the framework of the general non-perturbative and non-Markovian formulations. A preliminary semi-classical perturbation-theory treatment of the electromagnetic interaction is adopted. However, it is emphasized that a quantized-electromagnetic-field approach will be necessary for a fully self-consistent quantum-mechanical formulation. The primary quantities of interest are the linear and the non-linear macroscopic electromagnetic-response tensors. Coherent initial electronic excitations and the full tetradic-matrix form of the Liouville-space self-energy operator representing the environmental interactions in the Markov approximation can incorporated in the expressions for these macroscopic electromagnetic-response tensors. Collisional interactions can be treated in various approximations for the Liouville-space self-energy operator, and the influence of Zeeman coherences on the macroscopic electromagnetic response can be investigated.