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dc.contributor.authorLewin, Mathieu
dc.contributor.authorNam, Phan Thành
dc.contributor.authorRougerie, Nicolas
dc.date.accessioned2019-03-25T12:42:28Z
dc.date.available2019-03-25T12:42:28Z
dc.date.issued2019
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18560
dc.language.isoenen
dc.subjectNonlinear Gibbsen
dc.subjectnonlinear Schrödinger-type classical field theoryen
dc.subject.ddc515en
dc.titleClassical field theory limit of 2D many-body quantum Gibbs statesen
dc.typeDocument de travail / Working paper
dc.description.abstractenNonlinear Gibbs measures play an important role in many areas of mathematics, including nonlinear dispersive equations with random initial data and stochastic partial differential equations. In statistical physics, they are believed to emerge for some quantum systems at criticality. In space dimensions two or larger, the measures are concentrated on singular distributions and they have to be be appropriately renormalized.In this paper we provide the first rigorous derivation of these renormalized nonlinear Gibbs measures in two space dimensions, starting from a linear quantum system in a mean-field-type limit. More precisely, we consider the grand-canonical Gibbs state of a large 2D bosonic quantum system and prove that it converges to the renormalized Gibbs measure of a nonlinear Schrödinger-type classical field theory. Reduced density matrices of the quantum Gibbs state converge to their classical analogues. The quantum system is well defined without any renormalization. By only tuning its chemical potential, we obtain a counter-term for the diverging repulsive interactions which provides the desired Wick renormalization of the limit classical theory.en
dc.publisher.nameCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages87en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01898563en
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2019-01
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2019-03-25T12:38:55Z
hal.person.labIds60
hal.person.labIds134862
hal.person.labIds688


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