Perturbations to the Laughlin state are accounted for by adding uncorrelated quasi-holes to the wave function.
Some contributions to many-body quantum mathematics
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abstract
The results summarized here are intended as rigorous mathematical statements on various physical models coming from condensed matter physics, statistical mechanics (classical and quantum), quantum field theory and cold atoms physics. The main tools are mostly those of the mathematical analyst: partial differential equations, functional analysis, spectral theory, calculus of variations, with some incursions into probability theory. A running thread is the construction, by rigorous asymptotic analysis most of the time, of bridges between different levels of mathematical modeling of physical phenomena. This is the manuscript for the author's habilitation thesis, summarizing results obtained between 2011 and 2016, in collaboration with: Michele Correggi, Mathieu Lewin, Douglas Lundholm, Phan Th\`anh Nam, Robert Seiringer, Sylvia Serfaty and Jakob Yngvason.
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On the Laughlin function and its perturbations
Perturbations to the Laughlin state are accounted for by adding uncorrelated quasi-holes to the wave function.