# Exceptional Points of Infinite Order Giving a Continuous Spectrum

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## 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## References

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