Focusing Gibbs measures with harmonic potential
Probability
2022-12-23 v1
Abstract
In this paper, we study the Gibbs measures associated to the focusing nonlinear Schr\"odinger equation with harmonic potential on Euclidean spaces. We establish a dichotomy for normalizability vs non-normalizability in the one dimensional case, and under radial assumption in the higher dimensional cases. In particular, we complete the programs of constructing Gibbs measures in the presence of a harmonic potential initiated by Burq-Thomann-Tzvetkov (2005) in dimension one and Deng (2013) in dimension two with radial assumption.
Cite
@article{arxiv.2212.11386,
title = {Focusing Gibbs measures with harmonic potential},
author = {Tristan Robert and Kihoon Seong and Leonardo Tolomeo and Yuzhao Wang},
journal= {arXiv preprint arXiv:2212.11386},
year = {2022}
}
Comments
31 pages