Mathematical and Physical Meaning of the Crossings of Energy Levels in \({\mathscr {PT}}\)-Symmetric Systems

  • Denis I. Borisov
  • Miloslav ZnojilEmail author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 184)


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.


Phase Transition Quantum Phase Transition Dynamical Regime Real Spectrum Exceptional Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of Mathematics CC USC RASUfaRussia
  2. 2.Bashkir State Pedagogical UniversityUfaRussia
  3. 3.University of Hradec KraloveHrader KraloveCzech Republic
  4. 4.Nuclear Physics Institute ASCRŘežCzech Republic

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