Gibbs measures based on 1d (an)harmonic oscillators as mean-field limits. (English) Zbl 1392.82023
Authors’ 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.
Reviewer: Anthony D. Osborne (Keele)
MSC:
| 82B30 | Statistical thermodynamics |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 46E39 | Sobolev (and similar kinds of) spaces of functions of discrete variables |
| 81V70 | Many-body theory; quantum Hall effect |
Keywords:
Gibbs measures; nonlinear Schrödinger functional; sub-harmonic trapping; boson; Sobolev space; density matrix; Hilbert-ScmidtReferences:
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