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Multiply Degenerate Exceptional Points and Quantum Phase Transitions

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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.

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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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Authors and Affiliations

  1. Institute of Mathematics CS USC RAS, Chernyshevskii str., 112, Ufa, 450008, Russia

    Denis I. Borisov

  2. Bashkir State Pedagogical University, October Rev. st., 3a, Ufa, 450000, Russia

    Denis I. Borisov

  3. Nuclear Physics Institute ASCR, Hlavní 130, 250 68, Řež, Czech Republic

    František Ružička & Miloslav Znojil

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  1. Denis I. Borisov
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  2. František Ružička
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  3. Miloslav Znojil
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Correspondence to Miloslav Znojil.

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Borisov, D.I., Ružička, F. & Znojil, M. Multiply Degenerate Exceptional Points and Quantum Phase Transitions. Int J Theor Phys 54, 4293–4305 (2015). https://doi.org/10.1007/s10773-014-2493-y

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  • DOI: https://doi.org/10.1007/s10773-014-2493-y

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