Isotropic polynomial invariants of Hall tensor

Jinjie Liu; Weiyang Ding; Liqun Qi; Wennan Zou

doi:10.1007/s10483-018-2398-9

Isotropic polynomial invariants of Hall tensor

Jinjie Liu, Weiyang Ding, Liqun Qi, Wennan Zou

Research output: Journal article publication › Journal article › Academic research › peer-review

5 Citations (Scopus)

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. 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.

Original language	English
Pages (from-to)	1845-1856
Number of pages	12
Journal	Applied Mathematics and Mechanics (English Edition)
Volume	39
Issue number	12
DOIs	https://doi.org/10.1007/s10483-018-2398-9
Publication status	Published - 1 Dec 2018

Keywords

function basis
Hall tensor
integrity basis
irreducibility
isotropic polynomial invariant
O29

ASJC Scopus subject areas

Mechanics of Materials
Mechanical Engineering
Applied Mathematics

More information

10.1007/s10483-018-2398-9

Cite this

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AU - Ding, Weiyang

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AU - Zou, Wennan

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AB - 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.

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KW - Hall tensor

KW - integrity basis

KW - irreducibility

KW - isotropic polynomial invariant

KW - O29

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JO - Applied Mathematics and Mechanics (English Edition)

JF - Applied Mathematics and Mechanics (English Edition)

IS - 12

ER -

Isotropic polynomial invariants of Hall tensor

Abstract

Keywords

ASJC Scopus subject areas

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