Dielectric polarization: a problem in the physics of an open system

Properties of extended systems that depend upon the electronic position coordinate, electric or magnetic polarization, permanent or induced, require the physics of an open system for their statement and solution. The treatment of an extended system as a collection of cells defined as bounded regions of real space necessarily leads to the inclusion of a contribution to the polarization arising from the transfer of charge across or from the flux in current through a cell's boundary, in addition to its internal polarization. The measurement of electric polarization in terms of the time integral of an induced current for a set of unit cells of arbitrary size within a crystal is shown to include a contribution from the flux in the position weighted current through its boundary. A crystal whose induced current is measured in a shorted capacitor is a macroscopic open system, and in this case it is the flux in the position weighted current through the surfaces that the crystal shares with the plates of the capacitor that contributes to the measured polarization. The present approach, stated in terms of the electron density and its current, challenges the philosophy underlying the 'modern theory of polarization' (MTP), which contends that the polarization of a dielectric can be achieved only by shifting the problem from one stated in terms of the electron density to one stated in terms of the phase of the wavefunction. The paper reviews the derivation of the defining equations of macroscopic polarization and magnetization from Maxwell's equations of classical electrodynamics and their use in MTP. Attention is drawn to the omission in these derivations of the contributions from the fluxes in the electric field and currents through the surfaces of the constituent subsystems, as required by the physics of an open system.