Isotropic Polynomial Invariants of the Hall Tensor
Mathematical Physics
2018-06-19 v3 math.MP
Abstract
The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third order and three dimensional, whose first two indices are skew-symmetric. In this paper, we investigate the isotropic polynomial invariants of the Hall tensor by connecting it with a second order tensor via the third order Levi-Civita tensor. We propose a minimal isotropic integrity basis with 10 invariants for the Hall tensor. Furthermore, we prove that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.
Cite
@article{arxiv.1712.03658,
title = {Isotropic Polynomial Invariants of the Hall Tensor},
author = {Jinjie Liu and Weiyang Ding and Liqun Qi and Wennan Zou},
journal= {arXiv preprint arXiv:1712.03658},
year = {2018}
}