发表机构
Universitá di Genova; I.N.F.N. - Sezione di Genova（热那亚大学; 意大利国家核物理研究所热那亚分部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明仅对称性不足以保证SK有效场论中非高斯噪声顶点的概率解释，推导出最优累积量界，给出构造性正分布、闭式响应与精确采样算法，并应用于布朗粒子模型与全息噪声顶点检验。
AI 中文摘要
基于Schwinger-Keldysh（SK）形式构建的现代耗散流体动力学有效场论，包含了非高斯的热噪声。由此产生的高阶噪声顶点受对称性约束，但除此之外被视为自由参数。我们明确证明，仅靠对称性约束并不能保证这些顶点产生真实的概率分布。要求具有概率解释，会在累积量之间产生尖锐的界，而这些界在对称性分析中是看不见的。这些界是最优的：其边界由显式的正分布达到，并且为负峰度和正峰度噪声数据都提供了构造性补全。这给出了闭式非线性响应和精确采样算法，其蒙特卡洛实现重现了精确的累积量和非线性涨落耗散关系。与微观结果对比时，该框架对文献中使用的布朗粒子四次模型的正随机补全所需的时间步长给出了尖锐下界，而全息计算的$SU(2)$噪声顶点通过了非平凡的连续四阶正性检验。
英文摘要
Modern effective field theories of dissipative hydrodynamics, built on the Schwinger-Keldysh (SK) formalism, include thermal noise that is not Gaussian. The resultant higher-order noise vertices are constrained by symmetries, but otherwise treated as free parameters. We show explicitly that symmetry constraints alone do not guarantee these vertices yield a genuine probability distribution. Requiring a probability interpretation yields sharp bounds between cumulants that are invisible to the symmetry analysis. The bounds are optimal: their boundaries are attained by explicit positive distributions, and constructive completions are provided for both negative- and positive-kurtosis noise data. This gives closed-form nonlinear response and an exact sampling algorithm, whose Monte Carlo implementation reproduces the exact cumulants and nonlinear fluctuation-dissipation relations. Confronted with microscopic results, the framework places a sharp lower bound on the time step required for a positive stochastic completion of a quartic model of the Brownian particle used in the literature, while holographically computed $SU(2)$ noise vertices pass a nontrivial continuum fourth-order positivity test.
Comments6 pages, 2 figures + 12 pages supplemental material, v2 - missing supplementary material internal references added, citations updated
