Gibbs measures based on 1D (an)harmonic oscillators as mean-field limits
Lewin, Mathieu; Nam, Phan Thành; Rougerie, Nicolas (2018), Gibbs measures based on 1D (an)harmonic oscillators as mean-field limits, Journal of Mathematical Physics, 59, p. n°041901. 10.1063/1.5026963
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01496137
Journal nameJournal of Mathematical Physics
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Abstract (EN)We prove that Gibbs measures based on 1D defocusing nonlinear Schrödinger functionals with sub-harmonic trapping can be obtained as the mean-field/large temperature limit of the corresponding grand-canonical ensemble for many bosons. The limit measure is supported on Sobolev spaces of negative regularity and the corresponding density matrices are not trace-class. The general proof strategy is that of a previous paper of ours, but we have to complement it with Hilbert-Schmidt estimates on reduced density matrices.
Subjects / KeywordsMathématiques; Physique mathématique; Gibbs measures; mean-field limits
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