Pseudo-chirality: a manifestation of Noether's theorem in non-Hermitian systems

• URL: http://arxiv.org/abs/2101.09239v1
• Date: Fri, 22 Jan 2021 17:51:15 GMT
• Title: Pseudo-chirality: a manifestation of Noether's theorem in non-Hermitian systems
• Authors: Jose D. H. Rivero and Li Ge
• Abstract summary: We reveal previously unidentified constants of motion in non-Hermitian systems with parity-time and chiral symmetries. We discuss previously unidentified symmetries of this non-Hermitian topological system, and we reveal how its constant of motion due to pseudo-chirality can be used as an indicator of whether a pure chiral edge state is excited.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Noether's theorem relates constants of motion to the symmetries of the system. Here we investigate a manifestation of Noether's theorem in non-Hermitian systems, where the inner product is defined differently from quantum mechanics. In this framework, a generalized symmetry which we term pseudo-chirality emerges naturally as the counterpart of symmetries defined by a commutation relation in quantum mechanics. Using this observation, we reveal previously unidentified constants of motion in non-Hermitian systems with parity-time and chiral symmetries. We further elaborate the disparate implications of pseudo-chirality induced constant of motion: It signals the pair excitation of a generalized "particle" and the corresponding "hole" but vanishes universally when the pseudo-chiral operator is anti-symmetric. This disparity, when manifested in a non-Hermitian topological lattice with the Landau gauge, depends on whether the lattice size is even or odd. We further discuss previously unidentified symmetries of this non-Hermitian topological system, and we reveal how its constant of motion due to pseudo-chirality can be used as an indicator of whether a pure chiral edge state is excited.

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