Nonrelativistic ChernSimons vortices on the torus
Abstract
A classification of all periodic selfdual static vortex solutions of the JackiwPi model is given. Physically acceptable solutions of the Liouville equation are related to a class of functions, which we term Ωquasielliptic. This class includes, in particular, the elliptic functions and also contains a function previously investigated by Olesen. Some examples of solutions are studied numerically and we point out a peculiar phenomenon of lost vortex charge in the limit where the period lengths tend to infinity, that is, in the planar limit.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 July 2011
 DOI:
 10.1063/1.3610643
 arXiv:
 arXiv:0912.0718
 Bibcode:
 2011JMP....52g2901A
 Keywords:

 ChernSimons theory;
 Liouville equation;
 11.15.Yc;
 02.60.Nm;
 Integral and integrodifferential equations;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Number Theory
 EPrint:
 25 pages, 2+3 figures