TY - JOUR
T1 - Isotropic polynomial invariants of Hall tensor
AU - Liu, Jinjie
AU - DING, Weiyang
AU - Qi, Liqun
AU - Zou, Wennan
N1 - Funding Information:
∗ Citation: LIU, J. J., DING, W. Y., QI, L. Q., and ZOU, W. N. Isotropic polynomial invariants of Hall tensor. Applied Mathematics and Mechanics (English Edition), 39(12), 1845–1856 (2018) https://doi.org/10.1007/s10483-018-2398-9 † Corresponding author, E-mail: [email protected] 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), and the National Natural Science Foundation of China (No. 11372124) ©c Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018
PY - 2018/12/1
Y1 - 2018/12/1
N2 - 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.
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.
KW - function basis
KW - Hall tensor
KW - integrity basis
KW - irreducibility
KW - isotropic polynomial invariant
KW - O29
UR - http://www.scopus.com/inward/record.url?scp=85056117904&partnerID=8YFLogxK
U2 - 10.1007/s10483-018-2398-9
DO - 10.1007/s10483-018-2398-9
M3 - Journal article
AN - SCOPUS:85056117904
SN - 0253-4827
VL - 39
SP - 1845
EP - 1856
JO - Applied Mathematics and Mechanics (English Edition)
JF - Applied Mathematics and Mechanics (English Edition)
IS - 12
ER -