Isotropic polynomial invariants of Hall tensor  

作　　者：Jinjie LIU Weiyang DING Liqun QI Wennan ZOU 

机构地区：[1]Department of Applied Mathematics, The Hong Kong Polytechnic University [2]Department of Mathematics, Hong Kong Baptist University [3]Institute for Advanced Study, Nanchang University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2018年第12期1845-1856,共12页应用数学和力学（英文版）

基　　金：Project supported by Hong Kong Baptist University RC’s Start-up Grant for New Academics,the Hong Kong Research Grant Council(Nos.PolyU 15302114,15300715,15301716,and 15300717);the National Natural Science Foundation of China(No.11372124)

摘　　要：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. This paper investigates the isotropic polynomial invariants of the Hall tensor by connecting it with a second-order tensor via the third-order Levi-Civita tensor. A minimal isotropic integrity basis with 10 invariants for the Hall tensor is proposed. Furthermore, it is proved that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.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. This paper investigates the isotropic polynomial invariants of the Hall tensor by connecting it with a second-order tensor via the third-order Levi-Civita tensor. A minimal isotropic integrity basis with 10 invariants for the Hall tensor is proposed. Furthermore, it is proved that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.

关 键 词：isotropic polynomial invariant IRREDUCIBILITY function basis integrity basis Hall tensor 

分 类 号：O29[理学—应用数学]