Exceptional points of infinite order give a continuous spectrum

TL;DR

This paper demonstrates that infinite-order exceptional points in a matrix model lead to a continuous energy spectrum with non-norm-conserving states, revealing new spectral and dynamical phenomena at the limit of infinite order.

Contribution

It introduces a matrix model illustrating how infinite-order exceptional points produce a continuous spectrum and non-norm-conserving states, extending previous oscillator-based results.

Findings

States with real energies form a continuous spectrum at infinite order

Non-norm-conserving states appear near the exceptional point for large N

Characteristic time scale for nonconservation grows linearly with N

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.