The Landau Hamiltonian with δ-potentials supported on curves

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F20%3A00339702" target="_blank" >RIV/68407700:21340/20:00339702 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1142/S0129055X20500105" target="_blank" >https://doi.org/10.1142/S0129055X20500105</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0129055X20500105" target="_blank" >10.1142/S0129055X20500105</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Landau Hamiltonian with δ-potentials supported on curves

Popis výsledku v původním jazyce

The spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian Aα = (idel + A)2 + αδ ς in L2(ℝ2) with a δ-potential supported on a finite C1,1-smooth curve ς are studied. Here A = 1 2B(-x2,x1)τ is the vector potential, B > 0 is the strength of the homogeneous magnetic field, and α L) is a position-dependent real coefficient modeling the strength of the singular interaction on the curve. After a general discussion of the qualitative spectral properties of & and its resolvent, one of the main objectives in the present paper is a local spectral analysis of & near the Landau levels B(2q + 1), q ℕ0. Under various conditions on &, it is shown that the perturbation smears the Landau levels into eigenvalue clusters, and the accumulation rate of the eigenvalues within these clusters is determined in terms of the capacity of the support of . Furthermore, the use of Landau Hamiltonians with δ-perturbations as model operators for more realistic quantum systems is justified by showing that A can be approximated in the norm resolvent sense by a family of Landau Hamiltonians with suitably scaled regular potentials. 2020 World Scientific Publishing Company.

Název v anglickém jazyce

The Landau Hamiltonian with δ-potentials supported on curves

Popis výsledku anglicky

The spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian Aα = (idel + A)2 + αδ ς in L2(ℝ2) with a δ-potential supported on a finite C1,1-smooth curve ς are studied. Here A = 1 2B(-x2,x1)τ is the vector potential, B > 0 is the strength of the homogeneous magnetic field, and α L) is a position-dependent real coefficient modeling the strength of the singular interaction on the curve. After a general discussion of the qualitative spectral properties of & and its resolvent, one of the main objectives in the present paper is a local spectral analysis of & near the Landau levels B(2q + 1), q ℕ0. Under various conditions on &, it is shown that the perturbation smears the Landau levels into eigenvalue clusters, and the accumulation rate of the eigenvalues within these clusters is determined in terms of the capacity of the support of . Furthermore, the use of Landau Hamiltonians with δ-perturbations as model operators for more realistic quantum systems is justified by showing that A can be approximated in the norm resolvent sense by a family of Landau Hamiltonians with suitably scaled regular potentials. 2020 World Scientific Publishing Company.

Druh

J_imp - Článek v periodiku v databázi Web of Science

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

2020

Kód důvěrnosti údajů

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

Název periodika

Reviews in Mathematical Physics

ISSN

0129-055X

e-ISSN

1793-6659

Svazek periodika

32

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

47

Strana od-do

—

Kód UT WoS článku

000531487500002

EID výsledku v databázi Scopus

2-s2.0-85073877359