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Phenomenological Description
Published in Boris I. Sturman, Vladimir M. Fridkin, J.E.S. Bradley, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric Materials, 2021
Boris I. Sturman, Vladimir M. Fridkin, J.E.S. Bradley
The magnetophotovoltaic effect MPVE corresponds to the following current contribution [148]: ji(B)=J[SijkllBjekel*+QijlcBjKl],K→=i[e→e→*], in which B→ is the magnetic field; (1.52) is similar to (1.9). The pseudotensor Ŝ symmetrical with respect to the last two subscripts describes the linear MPVE, while the true tensor Q̂c describes the circular MPVE. The latter can occur in media where the circular PVE is absent. The magnetic field induces a circular current.
Symmetry arguments and the totalitarian principle in the physics of liquid crystals and other condensed matter systems
Published in Liquid Crystals, 2023
Tianyi Guo, Xiaoyu Zheng, Peter Palffy-Muhoray
To enable the construction of symmetry arguments, it is useful to note that all physical quantities may be regarded as tensors, tensors of different order, or rank. Scalars are tensors of rank 0, vectors are tensors of rank 1, quantities represented as matrices, such as linear polarisability, are tensors of rank 2 and so on. When using indicial notation, the number of indices that a tensor has is equal to its rank. A key notion is that all tensors are one of two types: they are either proper tensors, or they are pseudotensors. The type of a tensor is determined by its rank and the behaviour of the sign of its components under inversion. If the components of a tensor with even rank do not change sign on inversion, then the tensor is a proper tensor; if they change sign, then the tensor is a pseudotensor. Similarly, if the components of a tensor with odd rank change sign on inversion, then the tensor is a proper tensor; if they do not change sign, then the tensor is a pseudotensor. This is illustrated in Figure 1.