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International Journal of Theoretical Physics

, Volume 54, Issue 11, pp 3900–3906 | Cite as

Exceptional Points of Infinite Order Giving a Continuous Spectrum

  • Andrei Smilga
Article

Abstract

The observation in the title made earlier in association with the Pais–Uhlenbeck oscillator with equal frequencies is illustrated for an elementary matrix model. In the limit \(N \to \infty \) (N being the order of the exceptional point), an infinity of nontrivial states that do not change their norm during evolution appear. These states have real energies lying in a continuous interval. The norm of the “precursors” of these states at large finite N is not conserved, but the characteristic time scale where this nonconservation shows up grows linearly with N.

Keywords

Exceptional points Jordan blocks Continuous spectrum 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.SUBATECHUniversité de NantesNantesFrance

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