Systematics of quasi-Hermitian representations of non-Hermitian quantum models

0570860 - ÚJF 2024 RIV US eng J - Journal Article
Znojil, Miloslav
Systematics of quasi-Hermitian representations of non-Hermitian quantum models.
Annals of Physics. Roč. 448, JAN (2023), č. článku 169198. ISSN 0003-4916. E-ISSN 1096-035X
Institutional support: RVO:61389005
Keywords : non-Hermitian quantum mechanics of * unitary systems * Isospectral preconditionings of * Hamiltonians * Physical Hilbert spaces with ad hoc * inner-product metrics * Alternative reconstructions of hidden * Hermiticity
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 3, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.aop.2022.169198

In the currently quickly growing area of applications of non -Hermitian Hamiltonians H not equal H-dagger which are quasi-Hermitian (i.e., such that H-dagger Theta not equal Theta H, with a suitable inner-product metric Theta not equal I), the correct probabilistic interpretation of the model is needed. Achieved either in the Buslaev-Grecchi-inspired spirit (BGI, one factorizes Theta = Omega dagger Omega and reconstructs the conventional Her-mitian Hamiltonian, H -> gimel = Omega H Omega(-1) = gimel(dagger)) or in the much user-friendlier, Dyson-inspired spirit (DI, one eliminates the 'dif-ficult'reference to h via the quasi-Hermiticity rule, i.e., via an 'easier'reconstruction of Theta). Here, the two model-building BGI and DI recipes are identified as the two extreme special cases of a general correct-interpretation-providing strategy. We show that at any preselected integer N one may make a choice between the BGI extreme and an N-plet of the other, consistent and physical DI-type representations of the system in which a specific, partially modified Hamiltonian is constructed as quasi -Hermitian with respect to a specific, simplified inner-product metric. In applications, any one of these N+1 options may prove optimal for a given H: A schematic three-state quantum system is discussed as an illustrative example.
Permanent Link: https://hdl.handle.net/11104/0342188