Perturbation Theory Near Degenerate Exceptional Points

0532599 - ÚJF 2021 RIV CH eng J - Článek v odborném periodiku
Znojil, Miloslav
Perturbation Theory Near Degenerate Exceptional Points.
Symmetry-Basel. Roč. 12, č. 8 (2020), č. článku 1309. E-ISSN 2073-8994
Institucionální podpora: RVO:61389005
Klíčová slova: non-Hermitian quantum dynamics * unitary vicinity of exceptional points * degenerate perturbation theory * Hilbert-space geometry near EPs
Obor OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impakt faktor: 2.713, rok: 2020
Způsob publikování: Open access
https://doi.org/10.3390/sym12081309

In an overall framework of quantum mechanics of unitary systems a rather sophisticated new version of perturbation theory is developed and described. The motivation of such an extension of the list of the currently available perturbation-approximation recipes was four-fold: (1) its need results from the quick growth of interest in quantum systems exhibiting parity-time symmetry (PT-symmetry) and its generalizations. (2) in the context of physics, the necessity of a thorough update of perturbation theory became clear immediately after the identification of a class of quantum phase transitions with the non-Hermitian spectral degeneracies at the Kato's exceptional points (EP). (3) in the dedicated literature, the EPs are only being studied in the special scenarios characterized by the spectral geometric multiplicityLequal to one. (4) apparently, one of the decisive reasons may be seen in the complicated nature of mathematics behind the L >= 2 constructions. In our present paper we show how to overcome the latter, purely technical obstacle. The temporarily forgotten class of the L>1 models is shown accessible to a feasible perturbation-approximation analysis. In particular, an emergence of a counterintuitive connection between the value ofL, the structure of the matrix elements of perturbations, and the possible loss of the stability and unitarity of the processes of the unfolding of the singularities is given a detailed explanation.
Trvalý link: http://hdl.handle.net/11104/0311040