PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability
Journal Article
·
· Journal of Mathematical Physics
- 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)
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.
- Research Organization:
- Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- AC02-09CH11466
- OSTI ID:
- 1651133
- Journal Information:
- Journal of Mathematical Physics, Vol. 61, Issue 1; ISSN 0022-2488
- Publisher:
- American Institute of Physics (AIP)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
Cited by: 10 works
Citation information provided by
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