TY - JOUR

T1 - Behavior of eigenvalues in a region of broken PT symmetry

AU - Bender, Carl M.

AU - Hassanpour, Nima

AU - Hook, Daniel W.

AU - Klevansky, S. P.

AU - Sünderhauf, Christoph

AU - Wen, Zichao

N1 - Publisher Copyright:
© 2017 American Physical Society.

PY - 2017/5/15

Y1 - 2017/5/15

N2 - PT-symmetric quantum mechanics began with a study of the Hamiltonian H=p2+x2(ix)ϵ. When ϵ≥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, ϵ<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<ϵ<0. In particular, it reports the discovery of an infinite-order exceptional point at ϵ=-1, a transition from a discrete spectrum to a partially continuous spectrum at ϵ=-2, a transition at the Coulomb value ϵ=-3, and the behavior of the eigenvalues as ϵ approaches the conformal limit ϵ=-4.

AB - PT-symmetric quantum mechanics began with a study of the Hamiltonian H=p2+x2(ix)ϵ. When ϵ≥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, ϵ<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<ϵ<0. In particular, it reports the discovery of an infinite-order exceptional point at ϵ=-1, a transition from a discrete spectrum to a partially continuous spectrum at ϵ=-2, a transition at the Coulomb value ϵ=-3, and the behavior of the eigenvalues as ϵ approaches the conformal limit ϵ=-4.

UR - http://www.scopus.com/inward/record.url?scp=85026867673&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.95.052113

DO - 10.1103/PhysRevA.95.052113

M3 - Article

AN - SCOPUS:85026867673

SN - 2469-9926

VL - 95

JO - Physical Review A

JF - Physical Review A

IS - 5

M1 - 052113

ER -