<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this report we revisit the results obtained in [<xref ref-type="bibr" rid="j_awutp-2016-0006_ref_001_w2aab3b8b2b1b7b1ab1ab1Aa">1</xref>, <xref ref-type="bibr" rid="j_awutp-2016-0006_ref_002_w2aab3b8b2b1b7b1ab1ab2Aa">2</xref>] where the relativistic Aharonov-Bohm was studied for the first time. The method is based on the exact solutions of the complete (1+3)-dimensional Dirac equation of fermions moving in ideal Aharonov-Bohm (AB) rings and cylinders which are used for deriving the exact expressions of the relativistic partial currents. It is shown that these currents can be related to the derivative of the fermion energy with respect to the flux parameter, just as in the non-relativistic case. However, a new and remarkable relativistic effect is the saturation of the partial currents for high values of the total angular momentum. Based on this property, the total relativistic persistent currents at <italic>T</italic> = 0 is evaluated for rings and cylinders obtaining approximative simple closed formulas. Notice that this report brings together the texts of Refs. [<xref ref-type="bibr" rid="j_awutp-2016-0006_ref_001_w2aab3b8b2b1b7b1ab1ab1Aa">1</xref>, <xref ref-type="bibr" rid="j_awutp-2016-0006_ref_002_w2aab3b8b2b1b7b1ab1ab2Aa">2</xref>] with some improvements and unitary notations.</p></abstract>

In this report we revisit the results obtained in [1, 2] where the relativistic Aharonov-Bohm was studied for the first time. The method is based on the exact solutions of the complete (1+3)-dimensional Dirac equation of fermions moving in ideal Aharonov-Bohm (AB) rings and cylinders which are used for deriving the exact expressions of the relativistic partial currents. It is shown that these currents can be related to the derivative of the fermion energy with respect to the flux parameter, just as in the non-relativistic case. However, a new and remarkable relativistic effect is the saturation of the partial currents for high values of the total angular momentum. Based on this property, the total relativistic persistent currents at T = 0 is evaluated for rings and cylinders obtaining approximative simple closed formulas. Notice that this report brings together the texts of Refs. [1, 2] with some improvements and unitary notations.

Relativistic Persistent Currents in Ideal Aharonov-Bohm Rings and Cylinders

Annals of West University of Timisoara - Physics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Relativistic Persistent Currents in Ideal Aharonov-Bohm Rings and Cylinders"}

In this report we revisit the results obtained in [1, 2] where the relativistic Aharonov-Bohm was studied for the first time. The method is based on the exact...

Relativistic Persistent Currents in Ideal Aharonov-Bohm Rings and Cylinders

Published Online: Oct 23, 2017

Page range: 49 - 67

Received: Dec 03, 2016

Accepted: Dec 21, 2016

DOI: https://doi.org/10.1515/awutp-2016-0006

Keywords
Dirac equation, Aharonov-Bohm ring, Aharonov-Bohm cylinder, persistent current, saturation

© 2016 Ion I. Cotăescu, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Relativistic Persistent Currents in Ideal Aharonov-Bohm Rings and Cylinders

Published Online: Oct 23, 2017

Page range: 49 - 67

Received: Dec 03, 2016

Accepted: Dec 21, 2016

DOI: https://doi.org/10.1515/awutp-2016-0006

KeywordsDirac equation, Aharonov-Bohm ring, Aharonov-Bohm cylinder, persistent current, saturation

© 2016 Ion I. Cotăescu, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Dirac equation, Aharonov-Bohm ring, Aharonov-Bohm cylinder, persistent current, saturation