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arXiv · 1810.12991

Infinite energy solutions to vortex equations governing the fractional quantum Hall effect

Joseph Esposito
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Abstract

In this paper, we utilize weighted Sobolev spaces to establish an existence theory for infinite energy solutions to a coupled non-linear elliptic system. This system describes the fractional quantum Hall effect in two-dimensional double-layered systems. Via variational methods in a suitable weighted Sobolev space, we prove the existence of multiple vortices over the full plane. These methods include constrained minimization of an action functional and the existence of a critical point, known as a saddle point, by way of a mountain pass theorem. Furthermore, for these solutions, which are necessarily of infinite energy, we establish exponential decay estimates.

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Joseph Esposito. 2018-10-30. Infinite energy solutions to vortex equations governing the fractional quantum Hall effect. https://arxiv.org/abs/1810.12991

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