International Journal of Theoretical Physics

, Volume 54, Issue 12, pp 4293–4305 | Cite as

Multiply Degenerate Exceptional Points and Quantum Phase Transitions

  • Denis I. Borisov
  • František Ružička
  • Miloslav Znojil
Article

Abstract

The realization of a genuine phase transition in quantum mechanics requires that at least one of the Kato’s exceptional-point parameters becomes real. A new family of finite-dimensional and time-parametrized quantum-lattice models with such a property is proposed and studied. All of them exhibit, at a real exceptional-point time t = 0, the Jordan-block spectral degeneracy structure of some of their observables sampled by Hamiltonian H(t) and site-position Q(t). The passes through the critical instant t = 0 are interpreted as schematic simulations of non-equivalent versions of the Big-Bang-like quantum catastrophes.

Keywords

Quantum mechanics Cryptohermitian observables Spectra and pseudospectra Real exceptional points Phase transitions 

Notes

Acknowledgments

D.B. was partially supported by grant of RFBR, grant of President of Russia for young scientists-doctors of sciences (MD-183.2014.1) and Dynasty fellowship for young Russian mathematicians.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Denis I. Borisov
    • 1
    • 2
  • František Ružička
    • 3
  • Miloslav Znojil
    • 3
  1. 1.Institute of Mathematics CS USC RASUfaRussia
  2. 2.Bashkir State Pedagogical UniversityUfaRussia
  3. 3.Nuclear Physics Institute ASCRŘežCzech Republic

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