A random wave model for the Aharonov-Bohm effect

We study an ensemble of random waves subject to the Aharonov-Bohm effect. The introduction of a point with a magnetic flux of arbitrary strength into a random wave ensemble gives a family of wavefunctions whose distribution of vortices (complex zeros) is responsible for the topological phase associa...

Full description

Saved in:
Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2017-05, Vol.50 (20), p.205101
Main Authors: Houston, Alexander J H, Gradhand, Martin, Dennis, Mark R
Format: Article
Language:English
Subjects:
Aharonov-Bohm effect
magnetic flux
vortex correlations
wave vortices
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study an ensemble of random waves subject to the Aharonov-Bohm effect. The introduction of a point with a magnetic flux of arbitrary strength into a random wave ensemble gives a family of wavefunctions whose distribution of vortices (complex zeros) is responsible for the topological phase associated with the Aharonov-Bohm effect. Analytical expressions are found for the vortex number and topological charge densities as functions of distance from the flux point. Comparison is made with the distribution of vortices in the isotropic random wave model. The results indicate that as the flux approaches half-integer values, a vortex with the same sign as the fractional part of the flux is attracted to the flux point, merging with it in the limit of half-integer flux. We construct a statistical model of the neighbourhood of the flux point to study how this vortex-flux merger occurs in more detail. Other features of the Aharonov-Bohm vortex distribution are also explored.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/aa660f