Dynamic constitutive relations for polarization and magnetization - art. no. 056127

In this paper we develop constitutive relations for materials where the mag netization and polarization may depend on both the electric and magnetic fi elds. The approach is general, and is based on a previously developed stati stical-mechanical theory. We include the quadrupole-moment density as well as the dipole-moment density in the microscopic displacement field. This yi elds an electric gradient term in the constitutive equations. This leads to origin invariance in the multipole moments from which Maxwell's equations are defined. We present generalizations of Debye and Landau-Lifshitz equati ons of motion which are valid for nonequilibrium and contain memory. The re versible and relaxation terms in the polarization and magnetization evoluti on equations include the possibility of magnetoelectric coupling. Using con stitutive relationship, we derive evolution equations for the displacement and induction fields from a Hamiltonian approach.