The Landau Hamiltonian with delta-potentials supported on curves
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F20%3A00524523" target="_blank" >RIV/61389005:_____/20:00524523 - 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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
The Landau Hamiltonian with delta-potentials supported on curves
Popis výsledku v původním jazyce
The spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian A(alpha) = (i del + A)(2) + alpha delta(Sigma) in L-2(R-2) with a delta-potential supported on a finite C-1,C-1-smooth curve Sigma are studied. Here A = 1/2 B(-x(2), x(1))(T) is the vector potential, B > 0 is the strength of the homogeneous magnetic field, and alpha is an element of L-infinity(Sigma) is a position-dependent real coefficient modeling the strength of the singular interaction on the curve Sigma. After a general discussion of the qualitative spectral properties of A(alpha) and its resolvent, one of the main objectives in the present paper is a local spectral analysis of A(alpha) near the Landau levels B(2q + 1), q is an element of N-0. Under various conditions on alpha, 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 alpha. Furthermore, the use of Landau Hamiltonians with delta-perturbations as model operators for more realistic quantum systems is justified by showing that A(alpha) can be approximated in the norm resolvent sense by a family of Landau Hamiltonians with suitably scaled regular potentials.
Název v anglickém jazyce
The Landau Hamiltonian with delta-potentials supported on curves
Popis výsledku anglicky
The spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian A(alpha) = (i del + A)(2) + alpha delta(Sigma) in L-2(R-2) with a delta-potential supported on a finite C-1,C-1-smooth curve Sigma are studied. Here A = 1/2 B(-x(2), x(1))(T) is the vector potential, B > 0 is the strength of the homogeneous magnetic field, and alpha is an element of L-infinity(Sigma) is a position-dependent real coefficient modeling the strength of the singular interaction on the curve Sigma. After a general discussion of the qualitative spectral properties of A(alpha) and its resolvent, one of the main objectives in the present paper is a local spectral analysis of A(alpha) near the Landau levels B(2q + 1), q is an element of N-0. Under various conditions on alpha, 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 alpha. Furthermore, the use of Landau Hamiltonians with delta-perturbations as model operators for more realistic quantum systems is justified by showing that A(alpha) can be approximated in the norm resolvent sense by a family of Landau Hamiltonians with suitably scaled regular potentials.
Klasifikace
Druh
J<sub>imp</sub> - 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)
Návaznosti výsledku
Projekt
Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2020
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Reviews in Mathematical Physics
ISSN
0129-055X
e-ISSN
—
Svazek periodika
32
Číslo periodika v rámci svazku
4
Stát vydavatele periodika
SG - Singapurská republika
Počet stran výsledku
51
Strana od-do
2050010
Kód UT WoS článku
000531487500002
EID výsledku v databázi Scopus
2-s2.0-85073877359