Propagators associated to periodic Hamiltonians: an example of the Aharonov-Bohm Hamiltonian with two vortices
| dc.creator | Kocabova, P. | |
| dc.creator | Stovicek, P. | |
| dc.date | 2008-02-06 | |
| dc.date.accessioned | 2026-07-07T09:18:59Z | |
| dc.date.available | 2026-07-07T09:18:59Z | |
| dc.description | We consider an invariant quantum Hamiltonian $H=-Δ_{LB}+V$ in the $L^{2}$ space based on a Riemannian manifold $\tilde{M}$ with a discrete symmetry group $Γ$. Typically, $\tilde{M}$ is the universal covering space of a multiply connected manifold $M$ and $Γ$ is the fundamental group of $M$. To any unitary representation $Λ$ of $Γ$ one can relate another operator on $M=\tilde{M}/Γ$, called $H_Λ$, which formally corresponds to the same differential operator as $H$ but which 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 $H_Λ$ and $H$. Then we concentrate on the example of the Aharonov-Bohm effect with two vortices. We explain in detail the construction of the propagator in this case and indicate all essential intermediate steps. | |
| dc.identifier | https://arxiv.org/abs/0802.0755 | |
| dc.identifier | http://arxiv.org/abs/0802.0755 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154230 | |
| dc.subject | Mathematical Physics | |
| dc.title | Propagators associated to periodic Hamiltonians: an example of the Aharonov-Bohm Hamiltonian with two vortices | |
| dc.type | text |