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Journal of Mathematical Physics

Gibbs measures based on 1d (an)harmonic oscillators as mean-field limits

Mathieu Lewin B, Phan Thành Nam, Nicolas Rougerie

Published Apr 1, 2018• 19 citations
Publisher

Abstract

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.

DOI
10.1063/1.5026963

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The Euclidean ϕ24ϕ^4_2ϕ24​ theory as a limit of an inhomogeneous Bose gas
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