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arXiv · 1409.8450

Exceptional points of infinite order give a continuous spectrum

A. V. Smilga
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Abstract

The statement in the title discussed earlier in association with the Pais-Uhlenbeck oscillator with equal frequencies is illustrated for an elementary matrix model. In the limit when the order of the exceptional point N tends to infinity, 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.

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A. V. Smilga. 2014-09-30. Exceptional points of infinite order give a continuous spectrum. https://doi.org/10.1007/s10773-014-2404-2

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