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Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such "mesoscopic quantum electrodynamics" is shown to share its dynamical structure with the classical stochastic electrodynamics. In formal terms, we demonstrate that all general relations of the mesoscopic quantum electrodynamics may be recast in a form lacking Planck's constant. Mesoscopic quantum electrodynamics is therefore subject to "doing quantum electrodynamics while thinking classically," allowing one to substitute essentally classical considerations for quantum ones without any loss in generality. Implications of these results for the quantum measurement theory are discussed.

We have developed and implemented a formalism for computing the structural response of a periodic insulating system to a homogeneous static electric field within density-functional perturbation theory (DFPT). We consider the thermodynamic potentials E(R,eta,e) and F(R,eta,e) whose minimization with respect to the internal structural parameters R and unit cell strain eta yields the equilibrium structure at fixed electric field e and polarization P, respectively. First-order expansion of E(R,eta,e) in e leads to a useful approximation in which R(P) and eta(P) can be obtained by simply minimizing the zero-field internal energy with respect to structural coordinates subject to the constraint of a fixed spontaneous polarization P. To facilitate this minimization, we formulate a modified DFPT scheme such that the computed derivatives of the polarization are consistent with the discretized form of the Berry-phase expression. We then describe the application of this approach to several problems associated with bulk and short-period superlattice structures of ferroelectric materials such as BaTiO3 and PbTiO3. These include the effects of compositionally broken inversion symmetry, the equilibrium structure for high values of polarization, field-induced structural phase transitions, and the lattice contributions to the linear and the non-linear dielectric constants.