Propagators Associated to Periodic Hamiltonians

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F08%3A04150947" target="_blank" >RIV/68407700:21340/08:04150947 - isvavai.cz</a>

Result on the web

—

DOI - Digital Object Identifier

—

Result language

čeština

Original language name

Propagators Associated to Periodic Hamiltonians

Original language description

We consider an invariant quantum Hamiltonian $H=-Delta_{LB}+V$ in the $L^{2}$ space based on a Riemannian manifold $tilde{M}$ with a discrete symmetry group $Gamma$. Typically, $tilde{M}$ is the universal covering space of a multiply connected manifold $M$ and $Gamma$ is the fundamental group of $M$. To any unitary representation $Lambda$ of $Gamma$ one can relate another operator on $M=tilde{M}/Gamma$, called $H_Lambda$, which formally corresponds to the same differential operator as $H$ butwhich is determined by quasi-periodic boundary conditions. We give a brief review of the Bloch decomposition of $H$ and of a formula relating the propagators associated to the Hamiltonians $H_Lambda$ and $H$. Then we concentrate on the example of the Aharonov-Bohm effect with two vortices.

Czech name

Propagators Associated to Periodic Hamiltonians

Czech description

We consider an invariant quantum Hamiltonian $H=-Delta_{LB}+V$ in the $L^{2}$ space based on a Riemannian manifold $tilde{M}$ with a discrete symmetry group $Gamma$. Typically, $tilde{M}$ is the universal covering space of a multiply connected manifold $M$ and $Gamma$ is the fundamental group of $M$. To any unitary representation $Lambda$ of $Gamma$ one can relate another operator on $M=tilde{M}/Gamma$, called $H_Lambda$, which formally corresponds to the same differential operator as $H$ butwhich is determined by quasi-periodic boundary conditions. We give a brief review of the Bloch decomposition of $H$ and of a formula relating the propagators associated to the Hamiltonians $H_Lambda$ and $H$. Then we concentrate on the example of the Aharonov-Bohm effect with two vortices.

Type

D - Article in proceedings

CEP classification

BA - General mathematics

OECD FORD branch

—

Project

<a href="/en/project/GD202%2F08%2FH072" target="_blank" >GD202/08/H072: Mathematical structures in theoretical physics</a><br>

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2008

Confidentiality

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

Article name in the collection

Doktorandské dny 2008

ISBN

978-80-01-04195-6

ISSN

—

e-ISSN

—

Number of pages

11

Pages from-to

—

Publisher name

Česká technika - nakladatelství ČVUT

Place of publication

Praha

Event location

Praha

Event date

Nov 7, 2008

Type of event by nationality

CST - Celostátní akce

UT code for WoS article

—