PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability
Abstract
We prove that in finite dimensions, a Parity-Time (PT)-symmetric Hamiltonian is necessarily pseudo-Hermitian regard-less of whether it is diagonalizable or not. This result is different from Mostafazadeh’s, which requires the Hamiltonian to be diagonalizable. PT-symmetry breaking often occurs at exceptional points where the Hamiltonian is not diagonalizable. Our result implies that PT-symmetry breaking is equivalent to the onset of instabilities of pseudo-Hermitian systems, which was systematically studied by Krein et al. in 1950s. In particular, we show that the mechanism of PT-symmetry breaking is the resonance between two eigen modes with opposite signs of actions.
- Authors:
-
[1];
[2];
- Beijing Jiao Tong Univ. (China)
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Univ. of Science and Technology of China, Hefei (China)
- Univ. of Science and Technology of China, Hefei (China)
- Publication Date:
- Research Org.:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1651133
- Grant/Contract Number:
- AC02-09CH11466
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Mathematical Physics
- Additional Journal Information:
- Journal Volume: 61; Journal Issue: 1; Journal ID: ISSN 0022-2488
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Zhang, Ruili, Qin, Hong, and Xiao, Jianyuan. PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability. United States: N. p., 2020.
Web. doi:10.1063/1.5117211.
Zhang, Ruili, Qin, Hong, & Xiao, Jianyuan. PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability. United States. https://doi.org/10.1063/1.5117211
Zhang, Ruili, Qin, Hong, and Xiao, Jianyuan. Thu .
"PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability". United States. https://doi.org/10.1063/1.5117211. https://www.osti.gov/servlets/purl/1651133.
@article{osti_1651133,
title = {PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability},
author = {Zhang, Ruili and Qin, Hong and Xiao, Jianyuan},
abstractNote = {We prove that in finite dimensions, a Parity-Time (PT)-symmetric Hamiltonian is necessarily pseudo-Hermitian regard-less of whether it is diagonalizable or not. This result is different from Mostafazadeh’s, which requires the Hamiltonian to be diagonalizable. PT-symmetry breaking often occurs at exceptional points where the Hamiltonian is not diagonalizable. Our result implies that PT-symmetry breaking is equivalent to the onset of instabilities of pseudo-Hermitian systems, which was systematically studied by Krein et al. in 1950s. In particular, we show that the mechanism of PT-symmetry breaking is the resonance between two eigen modes with opposite signs of actions.},
doi = {10.1063/1.5117211},
journal = {Journal of Mathematical Physics},
number = 1,
volume = 61,
place = {United States},
year = {2020},
month = {1}
}
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