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Symmetry 2016, 8(6), 52; https://doi.org/10.3390/sym8060052

Parity-Time Symmetry and the Toy Models of Gain-Loss Dynamics near the Real Kato’s Exceptional Points

Nuclear Physics Institute of CAS, Hlavni 130, 250 68 Řež, Czech Republic
Academic Editor: Blas Manuel Rodríguez-Lara
Received: 16 May 2016 / Revised: 6 June 2016 / Accepted: 12 June 2016 / Published: 20 June 2016
(This article belongs to the Special Issue Parity-Time Symmetry in Optics and Photonics)
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Abstract

For a given operator D ( t ) of an observable in theoretical parity-time symmetric quantum physics (or for its evolution-generator analogues in the experimental gain-loss classical optics, etc.) the instant t c r i t i c a l of a spontaneous breakdown of the parity-time alias gain-loss symmetry should be given, in the rigorous language of mathematics, the Kato’s name of an “exceptional point”, t c r i t i c a l = t ( E P ) . In the majority of conventional applications the exceptional point (EP) values are not real. In our paper, we pay attention to several exactly tractable toy-model evolutions for which at least some of the values of t ( E P ) become real. These values are interpreted as “instants of a catastrophe”, be it classical or quantum. In the classical optical setting the discrete nature of our toy models might make them amenable to simulations. In the latter context the instant of Big Bang is mentioned as an illustrative sample of possible physical meaning of such an EP catastrophe in quantum cosmology. View Full-Text
Keywords: parity-time symmetry; Schrödinger equation; physical Hilbert space; inner-product metric operator; real exceptional points; solvable models; quantum Big Bang; quantum Inflation period parity-time symmetry; Schrödinger equation; physical Hilbert space; inner-product metric operator; real exceptional points; solvable models; quantum Big Bang; quantum Inflation period
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Znojil, M. Parity-Time Symmetry and the Toy Models of Gain-Loss Dynamics near the Real Kato’s Exceptional Points. Symmetry 2016, 8, 52.

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