Spectral analysis of the Dirac operator with a singular interaction on a broken line

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F24%3A00598052" target="_blank" >RIV/61389005:_____/24:00598052 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1063/5.0202693" target="_blank" >https://doi.org/10.1063/5.0202693</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/5.0202693" target="_blank" >10.1063/5.0202693</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Spectral analysis of the Dirac operator with a singular interaction on a broken line

Popis výsledku v původním jazyce

We consider the one-parametric family of self-adjoint realizations of the two-dimensional massive Dirac operator with a Lorentz scalar delta-shell interaction of strength tau is an element of R{-2,0,2} supported on a broken line of opening angle 2 omega with omega is an element of(0,pi/2). The essential spectrum of any such self-adjoint realization is symmetric with respect to the origin with a gap around zero whose size depends on the mass and, for tau < 0, also on the strength of the interaction, but does not depend on omega. As the main result, we prove that for any N is an element of N and strength tau is an element of (-infinity, 0){-2} the discrete spectrum of any such self-adjoint realization has at least N discrete eigenvalues, with multiplicities taken into account, in the gap of the essential spectrum provided that omega is sufficiently small. Moreover, we obtain an explicit estimate on omega sufficient for this property to hold. For tau is an element of (0, infinity){2}, the discrete spectrum consists of at most one simple eigenvalue.

Název v anglickém jazyce

Spectral analysis of the Dirac operator with a singular interaction on a broken line

Popis výsledku anglicky

We consider the one-parametric family of self-adjoint realizations of the two-dimensional massive Dirac operator with a Lorentz scalar delta-shell interaction of strength tau is an element of R{-2,0,2} supported on a broken line of opening angle 2 omega with omega is an element of(0,pi/2). The essential spectrum of any such self-adjoint realization is symmetric with respect to the origin with a gap around zero whose size depends on the mass and, for tau < 0, also on the strength of the interaction, but does not depend on omega. As the main result, we prove that for any N is an element of N and strength tau is an element of (-infinity, 0){-2} the discrete spectrum of any such self-adjoint realization has at least N discrete eigenvalues, with multiplicities taken into account, in the gap of the essential spectrum provided that omega is sufficiently small. Moreover, we obtain an explicit estimate on omega sufficient for this property to hold. For tau is an element of (0, infinity){2}, the discrete spectrum consists of at most one simple eigenvalue.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA21-07129S" target="_blank" >GA21-07129S: Nové jevy pocházející z narušení invariance vůči časové inversi</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Physics

ISSN

0022-2488

e-ISSN

1089-7658

Svazek periodika

65

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

24

Strana od-do

083514

Kód UT WoS článku

001299474200001

EID výsledku v databázi Scopus

2-s2.0-85202850343