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most citedSecond Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime

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math.AP2026

A Trichotomy for Modified Scattering Across the Yukawa-Coulomb Transition

Yonggeun Cho, Jinyeop Lee

We study the long-time asymptotics of the three-dimensional Hartree equation with Yukawa potential \[ V_μ(x)=\frac{e^{-μ|x|}}{|x|}, \qquad 0\leqμ\leq1. \] The Coulomb case correspo…