Dynamical confinement for Schrödinger operators with magnetic potential and Aharonov

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Dynamical confinement for Schrödinger operators with magnetic potential and Aharonov–Bohm effect

Published:2024-01-01 Issue:1 Volume:65 Page:
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:

Author:

de Oliveira C. R.¹^ORCID,Romano R. G.²^ORCID

Affiliation:

1. Departamento de Matemática, UFSCar 1 , São Carlos, SP 13560-970, Brazil

2. Departamento de Matemática, UFSC 2 , Blumenau, SC 89036-004, Brazil

Abstract

A magnetic potential is included in the so-called (quantum) dynamical confinement to open sets of Rd; gauge transformations are also discussed. Then, the results are applied to the Aharonov–Bohm model in the plane (the solenoid is a disk of radius greater than zero) in order to get some examples of operators confining the electron outside the solenoid.

Funder

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/5.0159003/18291913/012102_1_5.0159003.pdf

Reference40 articles.

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2. Significance of electromagnetic potentials in the quantum theory;Phys. Rev.,1959

3. High-velocity estimates for the scattering operator and Aharonov-Bohm effect in three dimensions;Commun. Math. Phys.,2009

4. Experimental test for approximately dispersionless forces in the Aharonov-Bohm effect;Europhys. Lett.,2016

5. Macroscopic test of the Aharonov-Bohm effect;Phys. Rev. Lett.,2007

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