An indefinite system of equations governing the fractional quantum Hall effect
Mathematical Physics
2018-10-19 v1 Mesoscale and Nanoscale Physics
math.MP
Abstract
In this paper, we establish existence of solutions to an indefinite coupled non-linear system. We use partial coercivity to establish existence of a critical point to an indefinite functional and thus the existence of solutions on both bounded domains and doubly-periodic domains. We then take the limit of the bounded domain to extend solutions on a bounded domain to the full-plane. We also provide asymptotic decay analysis for solutions over the full-plane. Necessary and sufficient conditions are also provided for the doubly periodic domain.
Keywords
Cite
@article{arxiv.1810.07723,
title = {An indefinite system of equations governing the fractional quantum Hall effect},
author = {Joseph Esposito},
journal= {arXiv preprint arXiv:1810.07723},
year = {2018}
}