Systematics of quasi-Hermitian representations of non-Hermitian quantum models
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F23%3A00570860" target="_blank" >RIV/61389005:_____/23:00570860 - isvavai.cz</a>
Alternative codes found
RIV/62690094:18470/23:50020912
Result on the web
<a href="https://doi.org/10.1016/j.aop.2022.169198" target="_blank" >https://doi.org/10.1016/j.aop.2022.169198</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aop.2022.169198" target="_blank" >10.1016/j.aop.2022.169198</a>
Alternative languages
Result language
angličtina
Original language name
Systematics of quasi-Hermitian representations of non-Hermitian quantum models
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annals of Physics
ISSN
0003-4916
e-ISSN
1096-035X
Volume of the periodical
448
Issue of the periodical within the volume
JAN
Country of publishing house
US - UNITED STATES
Number of pages
21
Pages from-to
169198
UT code for WoS article
000949984000001
EID of the result in the Scopus database
2-s2.0-85144397616