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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

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01496137
Date
2018
Journal name
Journal of Mathematical Physics
Number
59
Pages
n°041901
21
Publication identifier
Metadata
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Author(s)
Lewin, Mathieu cc

Nam, Phan Thành

Rougerie, Nicolas
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 / Keywords
Mathématiques; Physique mathématique; Gibbs measures; mean-field limits