Features, Paradoxes and Amendments of Perturbative Non-Hermitian Quantum Mechanics

0586598 - ÚJF 2025 RIV CH eng J - Journal Article
Znojil, Miloslav
Features, Paradoxes and Amendments of Perturbative Non-Hermitian Quantum Mechanics.
Symmetry-Basel. Roč. 16, č. 5 (2024), č. článku 629. E-ISSN 2073-8994
Institutional support: RVO:61389005
Keywords : unitary quantum mechanics * non-Hermitian Schrodinger picture * generalized perturbation theory * ambiguity of physical Hilbert space
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 2.7, year: 2022
Method of publishing: Open access
https://doi.org/10.3390/sym16050629

Quantum mechanics of unitary systems is considered in quasi-Hermitian representation and in the dynamical regime in which one has to take into account the ubiquitous presence of perturbations, random or specific. In this paper, it is shown that multiple technical obstacles encountered in such a context can be circumvented via just a mild amendment of the so-called Rayleigh-Schrodinger perturbation-expansion approach. In particular, the quasi-Hermitian formalism characterized by an enhancement of flexibility is shown to remain mathematically tractable while, on the phenomenological side, opening several new model-building horizons. It is emphasized that they include, i.a., the study of generic random perturbations and/or of multiple specific non-Hermitian toy models. In parallel, several paradoxes and open questions are shown to survive.
Permanent Link: https://hdl.handle.net/11104/0354052