English

Some contributions to many-body quantum mathematics

Mathematical Physics 2016-12-21 v2 Quantum Gases Analysis of PDEs math.MP Quantum Physics

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.

Keywords

Cite

@article{arxiv.1607.03833,
  title  = {Some contributions to many-body quantum mathematics},
  author = {Nicolas Rougerie},
  journal= {arXiv preprint arXiv:1607.03833},
  year   = {2016}
}

Comments

118 pages, "habilitation \`a diriger des recherches" thesis. The defense took place in Grenoble on November 8th, 2016. The composition of the committee has been added on the front page

R2 v1 2026-06-22T14:53:47.300Z