The Aharonov-Bohm Hamiltonian with two vortices revisited

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F16%3A00300669" target="_blank" >RIV/68407700:21340/16:00300669 - isvavai.cz</a>

Výsledek na webu

<a href="https://ojs.cvut.cz/ojs/index.php/ap/article/view/3105" target="_blank" >https://ojs.cvut.cz/ojs/index.php/ap/article/view/3105</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.14311/AP.2016.56.0224" target="_blank" >10.14311/AP.2016.56.0224</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Aharonov-Bohm Hamiltonian with two vortices revisited

Popis výsledku v původním jazyce

We consider an invariant quantum Hamiltonian H = -ΔLB + V in the L2 space based on a Riemannian manifold ˜M with a discrete symmetry group Γ. To any unitary representation Λ of Γ one can relate another operator on M = ˜M /Γ, called H_Λ, which formally corresponds to the same differential operator as H but which is determined by quasi-periodic boundary conditions. As originally observed by Schulman in theoretical physics and Sunada in mathematics, one can construct the propagator associated with H_Λ provided one knows the propagator associated with H. This approach is reviewed and demonstrated on a quantum model describing a charged particle on the plane with two Aharonov-Bohm vortices. The construction of the propagator is explained in full detail including all substantial intermediate steps.

Název v anglickém jazyce

The Aharonov-Bohm Hamiltonian with two vortices revisited

Popis výsledku anglicky

We consider an invariant quantum Hamiltonian H = -ΔLB + V in the L2 space based on a Riemannian manifold ˜M with a discrete symmetry group Γ. To any unitary representation Λ of Γ one can relate another operator on M = ˜M /Γ, called H_Λ, which formally corresponds to the same differential operator as H but which is determined by quasi-periodic boundary conditions. As originally observed by Schulman in theoretical physics and Sunada in mathematics, one can construct the propagator associated with H_Λ provided one knows the propagator associated with H. This approach is reviewed and demonstrated on a quantum model describing a charged particle on the plane with two Aharonov-Bohm vortices. The construction of the propagator is explained in full detail including all substantial intermediate steps.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA13-11058S" target="_blank" >GA13-11058S: Spektrální analýza operátorů a její aplikace v kvantové mechanice</a><br>

Návaznosti

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

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Acta Polytechnica

ISSN

1210-2709

e-ISSN

—

Svazek periodika

56

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

12

Strana od-do

224-235

Kód UT WoS článku

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EID výsledku v databázi Scopus

2-s2.0-84977564450