Interference of Non-Hermiticity with Hermiticity at Exceptional Points

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/62690094:18470/22:50020162

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Interference of Non-Hermiticity with Hermiticity at Exceptional Points

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Interference of Non-Hermiticity with Hermiticity at Exceptional Points

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematics

ISSN

2227-7390

e-ISSN

2227-7390

Svazek periodika

10

Číslo periodika v rámci svazku

20

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

23

Strana od-do

3721

Kód UT WoS článku

000873266800001

EID výsledku v databázi Scopus

2-s2.0-85140648300