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Focusing Gibbs measures with harmonic potential

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arxiv 2212.11386 v1 pith:D73KUFGZ submitted 2022-12-21 math.PR

Tristan Robert , Kihoon Seong , Leonardo Tolomeo , Yuzhao Wang This is my paper · ORCID
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keywords gibbsharmonicmeasurespotentialassumptiondimensiondimensionalfocusing
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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.

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  1. Gibbs measures as local equilibrium KMS states for focusing nonlinear Schr\"odinger equations

    math.AP 2024-12 conditional novelty 7.0 of 10

    Local KMS equilibrium states of focusing NLS and Hartree flows on T^d for d=1,2,3 coincide, on mass sublevel sets, with truncated Gibbs measures.

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