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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F19%3A00561421" target="_blank" >RIV/61389005:_____/19:00561421 - 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 delta-shell interactions

Popis výsledku v původním jazyce

In this article, Dirac operators A eta,tau coupled with combinations of electrostatic and Lorentz scalar delta -shell interactions of constant strength eta and tau, respectively, supported on compact surfaces Sigma subset of R3 are studied. In the rigorous definition of these operators, the delta -potentials are modeled by coupling conditions at Sigma. In the proof of the self-adjointness of A eta,tau, a Krein-type resolvent formula and a Birman-Schwinger principle are obtained. With their help, a detailed study of the qualitative spectral properties of A eta,tau is possible. In particular, the essential spectrum of A eta,tau 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 A eta,tau is computed and it is discussed that for some special interaction strengths, A eta,tau is decoupled to two operators acting in the domains with the common boundary Sigma.

Název v anglickém jazyce

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

Popis výsledku anglicky

In this article, Dirac operators A eta,tau coupled with combinations of electrostatic and Lorentz scalar delta -shell interactions of constant strength eta and tau, respectively, supported on compact surfaces Sigma subset of R3 are studied. In the rigorous definition of these operators, the delta -potentials are modeled by coupling conditions at Sigma. In the proof of the self-adjointness of A eta,tau, a Krein-type resolvent formula and a Birman-Schwinger principle are obtained. With their help, a detailed study of the qualitative spectral properties of A eta,tau is possible. In particular, the essential spectrum of A eta,tau 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 A eta,tau is computed and it is discussed that for some special interaction strengths, A eta,tau is decoupled to two operators acting in the domains with the common boundary Sigma.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

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

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

295-314

Kód UT WoS článku

000612865800003

EID výsledku v databázi Scopus

2-s2.0-85081344355