Publication details
Gibbs measures based on 1d (an)harmonic oscillators as mean-field limits
| Authors | |
|---|---|
| Year of publication | 2018 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Mathematical Physics |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1063/1.5026963 |
| 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. |