逆散射方法解决Kipnis-Marchioro-Presutti模型中非稳态热传递的全统计问题
Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
AI总结：
本文利用逆散射方法求解Kipnis-Marchioro-Presutti模型中非稳态热传递的全统计，获得精确大偏差函数并揭示非平凡对称关系。
摘要：
我们通过揭示并利用宏观涨落理论基本方程的完全可积性，确定了Kipnis-Marchioro-Presutti晶格气体模型在长时间极限下非稳态热传递的全统计。这些方程与导数非线性薛定谔方程（DNLS）密切相关，我们采用由Kaup和Newell（1978）为DNLS改编的Zakharov-Shabat逆散射方法（ISM）求解。对于初始局域热脉冲，我们获得了传递热量的精确大偏差函数的显式结果，并揭示了一个非平凡的对称关系。
英文摘要：
We determine the full statistics of nonstationary heat transfer in the Kipnis-Marchioro-Presutti lattice gas model at long times by uncovering and exploiting complete integrability of the underlying equations of the macroscopic fluctuation theory. These equations are closely related to the derivative nonlinear Schrödinger equation (DNLS), and we solve them by the Zakharov-Shabat inverse scattering method (ISM) adapted by Kaup and Newell (1978) for the DNLS. We obtain explicit results for the exact large deviation function of the transferred heat for an initially localized heat pulse, where we uncover a nontrivial symmetry relation.
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