Supersymmetry and Exceptional Points

0531571 - ÚJF 2021 RIV CH eng J - Journal Article
Znojil, Miloslav
Supersymmetry and Exceptional Points.
Symmetry-Basel. Roč. 12, č. 6 (2020), č. článku 892. E-ISSN 2073-8994
Institutional support: RVO:61389005
Keywords : hiddenly Hermitian quantum Hailtonians * Kato exceptional points * regularized singular potentials * hiddenly Hermitian supersymmetries * infinite family of regularized harmonic oscillators
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 2.713, year: 2020
Method of publishing: Open access
https://doi.org/10.3390/sym12060892

The phenomenon of degeneracy of energy levels is often attributed either to an underlying (super)symmetry (SUSY), or to the presence of a Kato exceptional point (EP). In our paper a conceptual bridge between the two notions is proposed to be provided by the recent upgrade of the basic principles of quantum theory called, equivalently,PT-symmetric or three-Hilbert-space (3HS) or quasi-Hermitian formulation in the current physical literature. Although the original purpose of the 3HS approach laid in the mere simplification of technicalities, it is shown here to serve also as a natural theoretical link between the apparently remote concepts of EPs and SUSY. An explicit illustration of their close mutual interplay is provided by the description of infinitely many supersymmetric, mutually non-equivalent and EP-separated regularized spiked harmonic oscillators.
Permanent Link: http://hdl.handle.net/11104/0310199