Focusing Gibbs measures with harmonic potential

Tristan Robert; Kihoon Seong; Leonardo Tolomeo; Yuzhao Wang

Focusing Gibbs measures with harmonic potential

Tristan Robert, Kihoon Seong, Leonardo Tolomeo, Yuzhao Wang

School of Mathematics

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In this paper, we study the Gibbs measures associated to the focusing nonlinear Schrödinger 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.

Original language	English
Journal	Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Publication status	Accepted/In press - 23 Dec 2022

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Focusing Gibbs measures with harmonic potentialAccepted author manuscript, 417 KB

https://arxiv.org/abs/2212.11386

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title = "Focusing Gibbs measures with harmonic potential",

abstract = "In this paper, we study the Gibbs measures associated to the focusing nonlinear Schr{\"o}dinger 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. ",

author = "Tristan Robert and Kihoon Seong and Leonardo Tolomeo and Yuzhao Wang",

year = "2022",

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T1 - Focusing Gibbs measures with harmonic potential

AU - Robert, Tristan

AU - Seong, Kihoon

AU - Tolomeo, Leonardo

AU - Wang, Yuzhao

PY - 2022/12/23

Y1 - 2022/12/23

N2 - In this paper, we study the Gibbs measures associated to the focusing nonlinear Schrödinger 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.

AB - In this paper, we study the Gibbs measures associated to the focusing nonlinear Schrödinger 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.

M3 - Article

JO - Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

JF - Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

ER -

Focusing Gibbs measures with harmonic potential

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