| Full text | |
| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] Univ Fed Sao Carlos, Dept Matemat, Sao Carlos, SP - Brazil
[2] UFSC, Ctr Ciencias Exatas & Educ, Blumenau, SC - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | Journal of Mathematical Physics; v. 58, n. 10 OCT 2017. |
| Web of Science Citations: | 1 |
| Abstract | |
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) | |
| FAPESP's process: | 12/21480-8 - Confirmation of the Aharonov-Bohm effect without interaction with the solenoid border |
| Grantee: | Renan Gambale Romano |
| Support Opportunities: | Scholarships in Brazil - Doctorate |