Two patterns of PT-symmetry breakdown in a non-numerical six-state simulation

0491118 - ÚJF 2019 RIV US eng J - Journal Article
Znojil, Miloslav - Borisov, D. I.
Two patterns of PT-symmetry breakdown in a non-numerical six-state simulation.
Annals of Physics. Roč. 394, č. 7 (2018), s. 40-49. ISSN 0003-4916. E-ISSN 1096-035X
R&D Projects: GA ČR GA16-22945S
Institutional support: RVO:61389005
Keywords : quantum theory * non-Hermitian observables * bound state instabilites * typology * discrete models
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 2.267, year: 2018

hree-parametric family of non-Hermitian but PT-symmetric six-by-six matrix Hamiltonians H-(6)(x, y, z) is considered. The PT-symmetry remains spontaneously unbroken (i.e., the spectrum of the bound-state energies remains real so that the unitary-evolution stability of the quantum system in question is shown guaranteed) in a non-empty domain D-(physical) of parameters x, y, z. The construction of the exceptional-point (EP) boundary partial derivative D-(physical) of the physical domain is preformed using an innovative non-numerical implicit-function-construction strategy. The topology of the resulting EP boundary of the spontaneous PT-symmetry breakdown (i.e., of the physical 'horizon of stability') is shown similar to its much more elementary N = 4 predecessor. Again, it is shown to consist of two components, viz., of the region of the quantum phase transitions of the first kind (during which at least some of the energies become complex) and of the quantum phase transitions of the second kind (during which some of the level pairs only cross but remain real).
Permanent Link: http://hdl.handle.net/11104/0285187