Publication details

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


NAM Phan Thanh LEWIN Mathieu ROUGERIE Nicolas

Year of publication 2018
Type Article in Periodical
Magazine / Source Journal of Mathematical Physics
MU Faculty or unit

Faculty of Science

Keywords Nonlinear Schrodinger-equation; reduced density-matrices; quantum continuous systems; global well-posedness; invariant-measures; thermodynamic limit; correlation inequalities; classical limit; gases property
Description We prove that Gibbs measures based on 1D defocusing nonlinear Schrodinger 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. Published by AIP Publishing.

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