Interference of Non-Hermiticity with Hermiticity at Exceptional Points
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F22%3A00563843" target="_blank" >RIV/61389005:_____/22:00563843 - isvavai.cz</a>
Alternative codes found
RIV/62690094:18470/22:50020162
Result on the web
<a href="https://doi.org/10.3390/math10203721" target="_blank" >https://doi.org/10.3390/math10203721</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math10203721" target="_blank" >10.3390/math10203721</a>
Alternative languages
Result language
angličtina
Original language name
Interference of Non-Hermiticity with Hermiticity at Exceptional Points
Original language description
The recent growth in popularity of the non-Hermitian quantum Hamiltonians H(lambda) with real spectra is strongly motivated by the phenomenologically innovative possibility of an access to the non-Hermitian degeneracies called exceptional points (EPs). What is actually presented in the present paper is a perturbation-theory-based demonstration of a fine-tuned nature of this access. This result is complemented by a toy-model-based analysis of the related details of quantum dynamics in the almost degenerate regime with lambda approximate to lambda(EP). In similar studies, naturally, one of the decisive obstacles is the highly nontrivial form of the underlying mathematics. Here, many of these obstacles are circumvented via several drastic simplifications of our toy models-i.a., our N by N matrices H(lambda)=H(N)(lambda) are assumed real, tridiagonal and PT-symmetric, and our H(N)(lambda) is assumed to be split into its Hermitian and non-Hermitian components staying in interaction. This is shown to lead to several remarkable spectral features of the model. Up to N=8, their description is even shown tractable non-numerically. In particular, it is shown that under generic perturbation, the 'unfolding' removal of the spontaneous breakdown of PT-symmetry proceeds via intervals of lambda with complex energy spectra.
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
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematics
ISSN
2227-7390
e-ISSN
2227-7390
Volume of the periodical
10
Issue of the periodical within the volume
20
Country of publishing house
CH - SWITZERLAND
Number of pages
23
Pages from-to
3721
UT code for WoS article
000873266800001
EID of the result in the Scopus database
2-s2.0-85140648300