Perturbation Theory Near Degenerate Exceptional Points

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017021" target="_blank" >RIV/62690094:18470/20:50017021 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61389005:_____/20:00532599

Výsledek na webu

<a href="https://www.mdpi.com/2073-8994/12/8/1309/htm" target="_blank" >https://www.mdpi.com/2073-8994/12/8/1309/htm</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/sym12081309" target="_blank" >10.3390/sym12081309</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Perturbation Theory Near Degenerate Exceptional Points

Popis výsledku v původním jazyce

In an overall framework of quantum mechanics of unitary systems a rather sophisticated new version of perturbation theory is developed and described. The motivation of such an extension of the list of the currently available perturbation-approximation recipes was four-fold: (1) its need results from the quick growth of interest in quantum systems exhibiting parity-time symmetry (PT-symmetry) and its generalizations; (2) in the context of physics, the necessity of a thorough update of perturbation theory became clear immediately after the identification of a class of quantum phase transitions with the non-Hermitian spectral degeneracies at the Kato&apos;s exceptional points (EP); (3) in the dedicated literature, the EPs are only being studied in the special scenarios characterized by the spectral geometric multiplicityLequal to one; (4) apparently, one of the decisive reasons may be seen in the complicated nature of mathematics behind the L &gt;= 2 constructions. In our present paper we show how to overcome the latter, purely technical obstacle. The temporarily forgotten class of the L&gt;1 models is shown accessible to a feasible perturbation-approximation analysis. In particular, an emergence of a counterintuitive connection between the value ofL, the structure of the matrix elements of perturbations, and the possible loss of the stability and unitarity of the processes of the unfolding of the singularities is given a detailed explanation.

Název v anglickém jazyce

Perturbation Theory Near Degenerate Exceptional Points

Popis výsledku anglicky

In an overall framework of quantum mechanics of unitary systems a rather sophisticated new version of perturbation theory is developed and described. The motivation of such an extension of the list of the currently available perturbation-approximation recipes was four-fold: (1) its need results from the quick growth of interest in quantum systems exhibiting parity-time symmetry (PT-symmetry) and its generalizations; (2) in the context of physics, the necessity of a thorough update of perturbation theory became clear immediately after the identification of a class of quantum phase transitions with the non-Hermitian spectral degeneracies at the Kato&apos;s exceptional points (EP); (3) in the dedicated literature, the EPs are only being studied in the special scenarios characterized by the spectral geometric multiplicityLequal to one; (4) apparently, one of the decisive reasons may be seen in the complicated nature of mathematics behind the L &gt;= 2 constructions. In our present paper we show how to overcome the latter, purely technical obstacle. The temporarily forgotten class of the L&gt;1 models is shown accessible to a feasible perturbation-approximation analysis. In particular, an emergence of a counterintuitive connection between the value ofL, the structure of the matrix elements of perturbations, and the possible loss of the stability and unitarity of the processes of the unfolding of the singularities is given a detailed explanation.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10302 - Condensed matter physics (including formerly solid state physics, supercond.)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

SYMMETRY-BASEL

ISSN

2073-8994

e-ISSN

—

Svazek periodika

12

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

17

Strana od-do

"Article Number: 1309"

Kód UT WoS článku

000567698700001

EID výsledku v databázi Scopus

—