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arXiv · 1810.07723

An indefinite system of equations governing the fractional quantum Hall effect

Joseph Esposito
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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.

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Joseph Esposito. 2018-10-17. An indefinite system of equations governing the fractional quantum Hall effect. https://arxiv.org/abs/1810.07723

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