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 alias Kato’s exceptional points (EP), its physical interpretation may 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.
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Acknowledgments
D.B. was supported by RFBR grant no. 14-01-97009-r_povolzhe_a. M.Z. was supported by RV O61389005 and by the GACR grant Nr. 16-22945S.
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Borisov, D.I., Znojil, M. (2016). Mathematical and Physical Meaning of the Crossings of Energy Levels in \({\mathscr {PT}}\)-Symmetric Systems. In: Bagarello, F., Passante, R., Trapani, C. (eds) Non-Hermitian Hamiltonians in Quantum Physics. Springer Proceedings in Physics, vol 184. Springer, Cham. https://doi.org/10.1007/978-3-319-31356-6_13
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DOI: https://doi.org/10.1007/978-3-319-31356-6_13
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