Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0810.0684 · Journal of Statistical Physics

Mathematical Justification of the Aharonov-Bohm Hamiltonian

César R. de Oliveira, Marciano Pereira

Published Nov 10, 2008• 31 citations
arXivHTMLPDF
DOI
10.1007/s10955-008-9631-y

Related papers

A mathematical model for the Aharonov-Bohm effect

Christiane Martin

Letters in Mathematical Physics•Mar 1, 1976•25 citations

On the Aharonov–Bohm Hamiltonian

Riccardo Adami, Alessandro Teta

Letters in Mathematical Physics•Jan 1, 1998•149 citations

Geometric phase of a classical Aharonov–Bohm Hamiltonian

Radha Balakrishnan, Indubala I. Satija

Physics Letters A•Mar 6, 2013•0 citations

Quadratic Forms for Aharonov-Bohm Hamiltonians

Davide Fermi

arXiv:2208.06285•Springer INdAM series•Jan 1, 2023•4 citations

The Aharonov-Bohm effect and variations

Barry R. Holstein

The subject of anholonomy in physics has recently been emphasized via discussions of the Berry phase. A particular example of this phenomenon, which does not require the adiabatic condition is the familiar Aharonov-Bohm (AB) effect. We herein review the AB effect and show that two additional phenomena, namely the Aharonov-Casher effect and rotating superconducting quantum interference device systems, can be analysed using identical mathematical frameworks.

Contemporary Physics•Mar 1, 1995•7 citations

Defect production by pure phase twist injection as Aharonov-Bohm effect

Matteo Foresti, Renzo L. Ricca

In this paper we demonstrate that new phase defects of the Gross-Pitaevskii equation (GPE) can be produced as a Aharonov-Bohm effect resulting from pure phase twist injection on existing defects. This is a phenomenon that has physical justification in the hydrodynamic interpretation of GPE. Here we give an analytical proof of its effects by using Fermi-Walker transport and Biot-Savart induction law. An analytical derivation of the dispersion relation is derived from the superposition of phase twist on the fundamental state. Since the extra twist corresponds to a topological change of the total linking number of the system, we show that the production of new defects is just another manifestation of the Aharonov-Bohm effect. We propose a laboratory experiment for Bose-Einstein condensates to test this phenomenon and to show that it can have useful applications in science and technology.

Physical review. E•Aug 16, 2019•10 citations
In this paper we demonstrate that new phase defects of the Gross-Pitaevskii equation (GPE) can be produced as a Aharonov-Bohm effect resulting from pure phase twist injection on existing defects. This is a phenomenon that has physical justification in the hydrodynamic interpretation of GPE. Here we give an analytical proof of its effects by using Fermi-Walker transport and Biot-Savart induction law. An analytical derivation of the dispersion relation is derived from the superposition of phase twist on the fundamental state. Since the extra twist corresponds to a topological change of the total linking number of the system, we show that the production of new defects is just another manifestation of the Aharonov-Bohm effect. We propose a laboratory experiment for Bose-Einstein condensates to test this phenomenon and to show that it can have useful applications in science and technology.