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arXiv · 1703.09422

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

Mathieu Lewin·Phan Thành Nam·Nicolas Rougerie
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Abstract

We prove that Gibbs measures based on 1D defocusing nonlinear Schr{ö}dinger 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.

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Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie. 2018-11-09. Gibbs measures based on 1D (an)harmonic oscillators as mean-field limits. https://arxiv.org/abs/1703.09422

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