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Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
Open accessAbstract
We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of pseudo-Hermitian Hamiltonians, and argue that the basic structure responsible for the particular spectral properties of these Hamiltonians is their pseudo-Hermiticity. We explore the basic properties of general pseudo-Hermitian Hamiltonians, develop pseudosupersymmetric quantum mechanics, and study some concrete examples, namely the Hamiltonian of the two-component Wheeler–DeWitt equation for the FRW-models coupled to a real massive scalar field and a class of pseudo-Hermitian Hamiltonians with a real spectrum.
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Cited by
Making sense of non-Hermitian Hamiltonians
Bender, C. M. (2007) · Reports on Progress in Physics · doi:10.1088/0034-4885/70/6/r03 · Cited by 2,984
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Regensburger, A., Bersch, C., Miri, M.-A., Onishchukov, G., Christodoulides, D. N., & Peschel, U. (2012) · Nature · doi:10.1038/nature11298 · Cited by 2,019
Exceptional topology of non-Hermitian systems
Bergholtz, E. J., Budich, J. C., & Kunst, F. K. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.015005 · Cited by 1,711
Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators
Chang, L., Jiang, X., Hua, S., Yang, C., Wen, J., Jiang, L., Li, G., Wang, G., & Xiao, M. (2014) · Nature Photonics · doi:10.1038/nphoton.2014.133 · Cited by 1,201
Yao, S., Song, F., & Wang, Z. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.136802 · Cited by 933
Metadata
- Authors
- Mostafazadeh, A.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 2002-01-01
- Volume
- 43
- Issue
- 1
- Pages
- 205-214
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2739884744
- Cited by
- 1,675
- References
- 0
- FWCI
- 38.95
- Type
- journal article
- Language
- en
- Open access
- green
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- Mostafazadeh, A. (2002). Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian. Journal of Mathematical Physics. https://doi.org/10.1063/1.1418246
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