Homogenization of the two-dimensional Hall effect

Abstract

In this paper, we study the two-dimensional Hall effect in a highly heterogeneous conducting material in the low magnetic field limit. Extending Bergman's approach in the framework of H-convergence we obtain the effective Hall coefficient which only depends on the corrector of the material resistivity in the absence of a magnetic field. A positivity property satisfied by the effective Hall coefficient is then deduced from the homogenization process. An explicit formula for the effective Hall coefficient is derived for anisotropic interchangeable two-phase composites.