Aharonov-Bohm effect without contact with the solenoid

Autor(es)

de Oliveira, Cesar R. ^[1] ; Romano, Renan G. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Carlos, Dept Matemat, Sao Carlos, SP - Brazil

^[2] UFSC, Ctr Ciencias Exatas & Educ, Blumenau, SC - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Physics; v. 58, n. 10 OCT 2017.
• Citações Web of Science: 1

Resumo

We add a scalar potential to the 2D Aharonov-Bohm (AB) model which properly diverges both at the solenoid border and at infinity so that the resulting operator is essentially self-adjoint and has a discrete spectrum; the former property is interpreted as no contact of the particle with the solenoid border since there is no need of boundary conditions. We study gauge transformations to get the usual periodic behavior of the AB properties as a function of the magnetic flux. The presence of the AB effect is proven through the ground state energy, which is shown to be smooth in case it is simple and with a nonzero derivative if the ground state is real valued; such properties are verified in the case of circular solenoids, for which it is shown to be a nonconstant periodic function with a minimum at integer and a maximum at half-integer circulations (at half-integer circulations, it is doubly degenerated). Published by AIP Publishing. (AU)

• Processo FAPESP: 12/21480-8 - Confirmação do efeito de Aharonov-Bohm sem interação com a fronteira do solenóide
• Beneficiário: Renan Gambale Romano
• Modalidade de apoio: Bolsas no Brasil - Doutorado