Vortex Lattice Solutions of the ZHK Chern-Simons Equations

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" Vortex Lattice Solutions of the ZHK Chern-Simons Equations "
Rajaratnam, Krishan Sigal, Israel M.

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	1105218
Doc. No	:	TLpq2303231109
Main Entry	:	Rajaratnam, Krishan
	:	Sigal, Israel M.
Title & Author	:	Vortex Lattice Solutions of the ZHK Chern-Simons Equations\ Rajaratnam, KrishanSigal, Israel M.
College	:	University of Toronto (Canada)
Date	:	2019
student score	:	2019
Degree	:	Ph.D.
Page No	:	66
Abstract	:	In this thesis we study the ZHK Chern-Simons equations which occur in the study of the fractional quantum hall effect of condensed matter physics. After stating basic properties of these equations, we first prove the existence of vortex lattice solutions of them. Among these solutions, we then find the lattice shape which minimizes the average energy per lattice cell. In addition to the vortex lattice solutions, we find solutions of the ZHK Chern-Simons equations on Riemann surfaces of higher genus g, by utilizing similar results for the Ginzburg-Landau equations. Finally, we study the orbital stability of the vortex lattice solutions under perturbations which preserve the lattice. Also, this thesis is based on results in two papers.
Subject	:	Mathematics
	:	Physics