Self-adjointness of the 2D Dirac Operator with Singular Interactions Supported on Star Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F23%3A00558934" target="_blank" >RIV/61389005:_____/23:00558934 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00023-022-01213-w" target="_blank" >https://doi.org/10.1007/s00023-022-01213-w</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00023-022-01213-w" target="_blank" >10.1007/s00023-022-01213-w</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Self-adjointness of the 2D Dirac Operator with Singular Interactions Supported on Star Graphs

Popis výsledku v původním jazyce

We consider the two-dimensional Dirac operator with Lorentz-scalar delta-shell interactions on each edge of a star graph. An orthogonal decomposition is performed which shows such an operator is unitarily equivalent to an orthogonal sum of half-line Dirac operators with off-diagonal Coulomb potentials. This decomposition reduces the computation of the deficiency indices to determining the number of eigenvalues of a one-dimensional spin-orbit operator in the interval (-1/2,1/2). If the number of edges of the star graph is two or three, these deficiency indices can then be analytically determined for a range of parameters. For higher numbers of edges, it is possible to numerically calculate the deficiency indices. Among others, examples are given where the strength of the Lorentz-scalar interactions directly change the deficiency indices, while other parameters are all fixed and where the deficiency indices are (2,2), neither of which have been observed in the literature to the best knowledge of the authors. For those Dirac operators which are not already self-adjoint and do not have 0 in the spectrum of the associated spin-orbit operator, the distinguished self-adjoint extension is also characterized.

Název v anglickém jazyce

Self-adjointness of the 2D Dirac Operator with Singular Interactions Supported on Star Graphs

Popis výsledku anglicky

We consider the two-dimensional Dirac operator with Lorentz-scalar delta-shell interactions on each edge of a star graph. An orthogonal decomposition is performed which shows such an operator is unitarily equivalent to an orthogonal sum of half-line Dirac operators with off-diagonal Coulomb potentials. This decomposition reduces the computation of the deficiency indices to determining the number of eigenvalues of a one-dimensional spin-orbit operator in the interval (-1/2,1/2). If the number of edges of the star graph is two or three, these deficiency indices can then be analytically determined for a range of parameters. For higher numbers of edges, it is possible to numerically calculate the deficiency indices. Among others, examples are given where the strength of the Lorentz-scalar interactions directly change the deficiency indices, while other parameters are all fixed and where the deficiency indices are (2,2), neither of which have been observed in the literature to the best knowledge of the authors. For those Dirac operators which are not already self-adjoint and do not have 0 in the spectrum of the associated spin-orbit operator, the distinguished self-adjoint extension is also characterized.

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

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

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Annales Henri Poincare

ISSN

1424-0637

e-ISSN

1424-0661

Svazek periodika

24

Číslo periodika v rámci svazku

JAN

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

43

Strana od-do

179-221

Kód UT WoS článku

000820575600002

EID výsledku v databázi Scopus

2-s2.0-85133494333