论文标题
吉普尼 - 统治模型中非组织传热的完整统计数据
Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
论文作者
论文摘要
我们从局部热分布开始时，在长时间以一个维度在一定程度上长时间研究了吉普尼 - 摩托比亚甲基 - 晶格晶格气模型中的非平稳热传递。在大尺度上，这种初始条件可以描述为delta功能，$ u（x，t = 0）=wδ（x）$。我们通过加热来表征该过程，并通过时间$ t $，$ t $，$ t $ j = \ int_x^\ int_x^\ infty u（x，x，t = t）\，dx \ ,, $$转移到指定点$ x = x $的右侧，并研究了完整的概率分布$ \ nathcal $ \ nathcal {p}（j，j，x，x，t）$。 $ x = 0 $的特定情况最近已解决[bettelheim \ textit {et al}。物理。莱特牧师。 \ textbf {128}，130602（2022）]。在固定的$ j $，作为$ x $的函数和$ t $的函数，分布$ \ Mathcal {p} $具有与单文件扩散中示踪剂的位置相同的长期动态缩放属性。在这里，我们通过利用KMP模型的宏观波动理论（MFT）的方程式并使用Zakharov-Shabat逆散射方法来评估$ \ MATHCAL {P}（J，X，T）$。我们还讨论了$ \ Mathcal {p}（j，x，t）$的渐近学，我们从精确解决方案中提取，并通过将两种不同的扰动方法直接应用于MFT方程来获得。
We investigate non-stationary heat transfer in the Kipnis-Marchioro-Presutti (KMP) lattice gas model at long times in one dimension when starting from a localized heat distribution. At large scales this initial condition can be described as a delta-function, $u(x,t=0)=W δ(x)$. We characterize the process by the heat, transferred to the right of a specified point $x=X$ by time $T$, $$ J=\int_X^\infty u(x,t=T)\,dx\,, $$ and study the full probability distribution $\mathcal{P}(J,X,T)$. The particular case of $X=0$ has been recently solved [Bettelheim \textit{et al}. Phys. Rev. Lett. \textbf{128}, 130602 (2022)]. At fixed $J$, the distribution $\mathcal{P}$ as a function of $X$ and $T$ has the same long-time dynamical scaling properties as the position of a tracer in a single-file diffusion. Here we evaluate $\mathcal{P}(J,X,T)$ by exploiting the recently uncovered complete integrability of the equations of the macroscopic fluctuation theory (MFT) for the KMP model and using the Zakharov-Shabat inverse scattering method. We also discuss asymptotics of $\mathcal{P}(J,X,T)$ which we extract from the exact solution, and also obtain by applying two different perturbation methods directly to the MFT equations.
