On Dirac operators in R3 with electrostatic and Lorentz scalar δ -shell interactions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F19%3A00339666" target="_blank" >RIV/68407700:21340/19:00339666 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s40509-019-00186-6" target="_blank" >https://doi.org/10.1007/s40509-019-00186-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s40509-019-00186-6" target="_blank" >10.1007/s40509-019-00186-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Dirac operators in R3 with electrostatic and Lorentz scalar δ -shell interactions

Popis výsledku v původním jazyce

In this article, Dirac operators Aη,τ coupled with combinations of electrostatic and Lorentz scalar δ-shell interactions of constant strength η and τ, respectively, supported on compact surfaces ΣcR3 are studied. In the rigorous definition of these operators, the δ-potentials are modeled by coupling conditions at Σ. In the proof of the self-adjointness of Aη,τ, a Krein-type resolvent formula and a Birman–Schwinger principle are obtained. With their help, a detailed study of the qualitative spectral properties of Aη,τ is possible. In particular, the essential spectrum of Aη,τ is determined, it is shown that at most finitely many discrete eigenvalues can appear, and several symmetry relations in the point spectrum are obtained. Moreover, the nonrelativistic limit of Aη,τ is computed and it is discussed that for some special interaction strengths, Aη,τ is decoupled to two operators acting in the domains with the common boundary Σ.

Název v anglickém jazyce

On Dirac operators in R3 with electrostatic and Lorentz scalar δ -shell interactions

Popis výsledku anglicky

In this article, Dirac operators Aη,τ coupled with combinations of electrostatic and Lorentz scalar δ-shell interactions of constant strength η and τ, respectively, supported on compact surfaces ΣcR3 are studied. In the rigorous definition of these operators, the δ-potentials are modeled by coupling conditions at Σ. In the proof of the self-adjointness of Aη,τ, a Krein-type resolvent formula and a Birman–Schwinger principle are obtained. With their help, a detailed study of the qualitative spectral properties of Aη,τ is possible. In particular, the essential spectrum of Aη,τ is determined, it is shown that at most finitely many discrete eigenvalues can appear, and several symmetry relations in the point spectrum are obtained. Moreover, the nonrelativistic limit of Aη,τ is computed and it is discussed that for some special interaction strengths, Aη,τ is decoupled to two operators acting in the domains with the common boundary Σ.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

<a href="/cs/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Centrum pokročilých aplikovaných přírodních věd</a><br>

Návaznosti

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

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Quantum Studies: Mathematics and Foundations

ISSN

2196-5609

e-ISSN

2196-5617

Svazek periodika

6

Číslo periodika v rámci svazku

March

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

20

Strana od-do

295-314

Kód UT WoS článku

000612865800003

EID výsledku v databázi Scopus

2-s2.0-85081344355