AI 中文总结
该研究针对传统理论仅适用于弱非线性多体系统平衡分布计算的局限，开发了基于广义能量均分原理的框架，通过数值模拟验证其对强非线性系统的准确性，贡献了强非线性系统平衡分布的有效计算方法。
AI 中文摘要
获取非线性系统的平衡分布对于准确计算宏观可观测量至关重要。传统理论修正通常局限于弱非线性情况，此时相互作用项可被视为有效不相关的微扰，且随机相位近似适用。在本通讯中，我们开发了一种基于广义能量均分原理确定平衡分布的框架。我们的方法在弱非线性区可恢复现有修正，且关键的是，对于微扰贡献变得相关、传统方法失效的强非线性区仍有效。对非线性薛定谔方程、Majda-McLaughlin-Tabak模型和费米-帕斯塔-乌拉姆-钦（Fermi-Pasta-Ulam-Tsingou）模型的数值模拟表明，该方法对强于传统理论可及一个数量级以上的非线性情况能给出准确修正。
英文摘要
Obtaining equilibrium distributions of nonlinear systems is essential for accurately computing macroscopic observables. Conventional theoretical corrections are typically limited to weak nonlinearities, where interaction terms can be treated as effectively uncorrelated perturbations and the random phase approximation applies. In this Letter, we develop a framework to determine equilibrium distributions based on the generalized energy equipartition principle. Our approach recovers existing corrections in the weakly nonlinear regime and, crucially, remains valid for strong nonlinearities, where perturbative contributions become correlated and conventional approaches break down. Numerical simulations of the nonlinear Schrödinger equation, the Majda-McLaughlin-Tabak model, and the Fermi-Pasta-Ulam-Tsingou model demonstrate accurate corrections for nonlinearities more than an order of magnitude stronger than those accessible to conventional theories.
Comments6 pages, 3 figures
