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Behavior of eigenvalues in a region of broken PT symmetry

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Title: Behavior of eigenvalues in a region of broken PT symmetry
Authors: Bender, CM
Hassanpour, N
Hook, DW
Klevansky, SP
Snderhauf, C
Wen, Z
Item Type: Journal Article
Abstract: 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.
Issue Date: 15-May-2017
Date of Acceptance: 28-Feb-2017
URI: http://hdl.handle.net/10044/1/52835
DOI: https://dx.doi.org/10.1103/PhysRevA.95.052113
ISSN: 1050-2947
Publisher: American Physical Society
Journal / Book Title: Physical Review A
Volume: 95
Issue: 5
Copyright Statement: ©2017 American Physical Society
Keywords: Science & Technology
Physical Sciences
Optics
Physics, Atomic, Molecular & Chemical
Physics
NON-HERMITIAN HAMILTONIANS
QUANTUM-MECHANICS
FIELD-THEORY
SYSTEM
math-ph
hep-th
math.MP
quant-ph
Publication Status: Published
Article Number: ARTN 052113
Appears in Collections:Physics
Theoretical Physics
Faculty of Natural Sciences



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