Abstract
A short resumé of the essentials of exceptional points of second order is given. We then concentrate on a discussion of specific features of exceptional points of third order. While general properties of these singularities have been expounded extensively in the literature, we here concentrate on some specific aspects, that is the occurrence of ‘hidden’ or ‘concealed’ third order exceptional points. They occur under specific circumstances when an apparent second order exceptional point is accompanied by a third eigenvalue being equal to the other two at the singularity.
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References
T. Kato, Perturbation Theory of Linear Operators (Springer, Berlin, 1966)
M.V. Berry, Curr. Sci. 67, 220 (1994)
J. Wiersig, S.W. Kim, M. Hentschel, Phys. Rev. A 78, 53809 (2008)
B. Dietz et al., Phys. Rev. E 75, 027201 (2007)
W.D. Heiss, Eur. Phys. J. D 60, 257 (2010)
N. Moiseyev, Non-Hermitian Quantum Mechanics (Cambridge University Press, Cambridge, 2011)
W.D. Heiss, H.L. Harney, Eur. Phys. J. D 17, 149 (2001)
C. Dembowski et al., Phys. Rev. Lett. 86, 787 (2001). Phys. Rev. Lett. 90, 034101 (2003)
W.D. Heiss, J. Phys. A 45, 444016 (2012)
C.M. Bender, S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998)
C.N. Yang, T.D. Lee, Phys. Rev. 87, 410 (1952)
W.D. Heiss, F.G. Scholtz, H.B. Geyer, J.Phys. A: Math. Gen. 38, 1843 (2005); W.D. Heiss, J.Phys. A: Math. Gen. 39, 10081 (2006)
W.D. Heiss, A.L. Sannino, Phys. Rev. A 43, 4159 (1991)
P. Ring, P. Schuck, The Nuclear Many Body Problem (Springer, New York, 1980)
T.H. Schucan, H.A. Weidenmüller, Ann. Phys. (NY) 73, 108 (1972)
W.D. Heiss, J. Phys. A: Math. Theor. 41, 244010 (2008)
G. Demange, E.-M. Graefe, J. Phys. A: Math. Theor. 45, 025303 (2012)
W.D. Heiss, H. Cartarius, G. Wunner, J. Main, J. Phys. A: Math. Theor. 46, 275307 (2013)
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Heiss, W.D. (2016). Some Features of Exceptional Points. In: Bagarello, F., Passante, R., Trapani, C. (eds) Non-Hermitian Hamiltonians in Quantum Physics. Springer Proceedings in Physics, vol 184. Springer, Cham. https://doi.org/10.1007/978-3-319-31356-6_18
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DOI: https://doi.org/10.1007/978-3-319-31356-6_18
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