Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Dynamic Constitutive Relations for Polarization and magnetization



James R. Baker-Jarvis, Pavel Kabos


New engineered artificial and metamaterials combine ferroelectrics, ferrites, wires, resonant rings, and ferromagnetic materials to obtain a desired response. In this paper we develop constitute relations for materials where the magnetization and polarization may depend on both the electric and magnetic fields. The approach is very general and is based on a previously developed statistical-mechanical theory. We include the quadrupole-moment density as well as the dipole-moment density in the displacement field. This leads to reference-position invariance in Maxwell's equations. Generalizations of Debye and Landau-Fifshitz equations of motion are presented which are valid for nonequilibrium and contain memory. The generalized equations are shown to consist of reversible and irreversible components. The reversible and relaxation terms in the polarization and magnetization evolution equations include the possibility of magnetoelectric coupling. We derive Maxwell's equations from a Hamiltonian approach using the constitutive relationships. We contrast chiral response of free charge traveling on a wire spiral with magnetoelectric response.
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)


constitutive relations, dielectric relaxation, magnetic, magnetic response, nonequilibrium, nonlinear, nonlinear response, projection operator, relaxation


Baker-Jarvis, J. and Kabos, P. (2001), Dynamic Constitutive Relations for Polarization and magnetization, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), [online], (Accessed June 23, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created September 30, 2001, Updated October 12, 2021