A random wave model for the Aharonov–Bohm effect

Alexander Houston, Martin Gradhand, Mark Dennis

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.
Original languageEnglish
Article number205101
JournalJournal of Physics A: Mathematical and Theoretical
Issue number20
Early online date26 Apr 2017
Publication statusPublished - 19 May 2017

Bibliographical note

arXiv: 1612.01839


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