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- Title
Exceptional Points of Infinite Order Giving a Continuous Spectrum.
- Authors
Smilga, Andrei
- 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.
- Subjects
CONTINUOUS spectrum (Atomic spectrum); HARMONIC oscillators; CONTINUOUS functions; PARITY nonconservation; NUCLEAR energy
- Publication
International Journal of Theoretical Physics, 2015, Vol 54, Issue 11, p3900
- ISSN
0020-7748
- Publication type
Article
- DOI
10.1007/s10773-014-2404-2