Mathematical and physical meaning of the crossings of energy levels in $\mathcal{P}\mathcal{T}-$symmetric systems

Abstract

Unavoided crossings of the energy levels due to a variation of a real parameter are studied. It is found that after the quantum system in question passes through one of its energy-crossing points {\it alias} Kato's exceptional points (EP), its physical interpretation may {\em dramatically} change even when the crossing energies themselves do not complexify. The anomalous physical phase-transition mechanism of the change is revealed, attributed to the EP-related mathematics and illustrated via several exactly solvable matrix toy models.

23 pp, 9 figures

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Cited by in corpus (2)

• Passage through exceptional point: Case study
• Dirichlet spectrum of the paradigm model of complex PT-symmetric potential: $V(x)=-(ix{)}^N$