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Invariant Gibbs measures and global strong solutions for nonlinear Schr\"odinger equations in dimension two

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abstract

We consider the defocusing nonlinear Schr\"odinger equation on $\mathbb{T}^2$ with Wick ordered power nonlinearity, and prove almost sure global well-posedness with respect to the associated Gibbs measure. The heart of the matter is the uniqueness of the solution as limit of solutions to canonically truncated systems. The invariance of the Gibbs measure under the global dynamics follows as a consequence. The proof relies on the novel idea of random averaging operators.

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math-ph 1

years

2025 1

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CONDITIONAL 1

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$\Phi^4_3$ Theory from many-body quantum Gibbs states

math-ph · 2025-02-07 · conditional · novelty 8.0

The Gibbs state of an interacting Bose gas on the three-dimensional torus is proven to converge, in a tuned semiclassical limit, to the renormalized Phi^4_3 measure.

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  • $\Phi^4_3$ Theory from many-body quantum Gibbs states math-ph · 2025-02-07 · conditional · none · ref 2025 · internal anchor

    The Gibbs state of an interacting Bose gas on the three-dimensional torus is proven to converge, in a tuned semiclassical limit, to the renormalized Phi^4_3 measure.