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Mathematical and physical meaning of the crossings of energy levels in ${\cal PT}-$symmetric systems

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.

preprint2015arXivOpen access
Denis I. BorisovMiloslav Znojil
math-phmath.MPquant-ph
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Denis I. BorisovMiloslav Znojil

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