Behavior of eigenvalues in a region of broken PT symmetry
PT-symmetric quantum mechanics began with a study of the Hamiltonian H=p2+x2(ix)ɛ. When ɛ≥0, the eigenvalues of this non-Hermitian Hamiltonian are discrete, real, and positive. This portion of parameter space is known as the region of unbroken PT symmetry. In the region of broken PT symmetry, ɛ<0...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
15 May 2017
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| In: |
Physical review
Year: 2017, Volume: 95, Issue: 5 |
| ISSN: | 2469-9934 |
| DOI: | 10.1103/PhysRevA.95.052113 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1103/PhysRevA.95.052113 Verlag, Volltext: https://link.aps.org/doi/10.1103/PhysRevA.95.052113 
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| Author Notes: | Carl M. Bender, Nima Hassanpour, Daniel W. Hook, S.P. Klevansky, Christoph Sünderhauf, and Zichao Wen |
| Summary: | PT-symmetric quantum mechanics began with a study of the Hamiltonian H=p2+x2(ix)ɛ. When ɛ≥0, the eigenvalues of this non-Hermitian Hamiltonian are discrete, real, and positive. This portion of parameter space is known as the region of unbroken PT symmetry. In the region of broken PT symmetry, ɛ<0, only a finite number of eigenvalues are real and the remaining eigenvalues appear as complex-conjugate pairs. The region of unbroken PT symmetry has been studied but the region of broken PT symmetry has thus far been unexplored. This paper presents a detailed numerical and analytical examination of the behavior of the eigenvalues for −4<ɛ<0. In particular, it reports the discovery of an infinite-order exceptional point at ɛ=−1, a transition from a discrete spectrum to a partially continuous spectrum at ɛ=−2, a transition at the Coulomb value ɛ=−3, and the behavior of the eigenvalues as ɛ approaches the conformal limit ɛ=−4. |
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| Item Description: | Gesehen am 10.12.2020 |
| Physical Description: | Online Resource |
| ISSN: | 2469-9934 |
| DOI: | 10.1103/PhysRevA.95.052113 |