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Invariant Gibbs measures for 1D NLS in a trap

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arxiv 2301.02544 v2 pith:FIJR4ZR6 submitted 2023-01-06 math.AP

Van Duong Dinh (UMPA-ENSL) , Nicolas Rougerie (UMPA-ENSL) This is my paper · ORCID
classification math.AP
keywords gibbsequationmeasuresinvariantaddressalmostassociatedbehaving
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We consider the one dimensional cubic nonlinear Schr{\"o}dinger equation with trapping potential behaving like |x| s (s > 1) at infinity. We construct Gibbs measures associated to the equation and prove that the Cauchy problem is globally well-posed almost surely on their support. Consequently, the Gibbs measure is indeed invariant under the flow of the equation. We also address the construction and invariance of canonical Gibbs measures, conditioned on the L 2 mass.

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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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