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

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.

arXiv comment5 pages, 3 figures, with separate Supplemental Materials

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• Extension of Noether's theorem in PT-symmetric systems and its experimental demonstration in an optical setup
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• Unitary Scattering Protected by Pseudo-Hermiticity
• Enhancement of signal-to-noise ratio at a high-order exceptional point of coherent perfect absorption
• Non-Hermitian systems with a real spectrum and selective skin effect
• Entanglement between uncoupled modes with time-dependent complex frequencies
• Effective size of a parity-time symmetric dimer
• Insight of the Green's function as a defect state in a boundary value problem
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