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Title: PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability

Journal Article · · Journal of Mathematical Physics
DOI: https://doi.org/10.1063/1.5117211 · OSTI ID:1651133
ORCiD logo [1]; ORCiD logo [2];  [3]
  1. Beijing Jiao Tong Univ. (China)
  2. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Univ. of Science and Technology of China, Hefei (China)
  3. 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
Citation Metrics:
Cited by: 10 works
Citation information provided by
Web of Science

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