发表机构
Centro Brasileiro de Pesquisas Físicas; Universidade Federal de Santa Catarina（巴西物理研究中心; 圣卡塔琳娜联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推导了$\beta$-FPUT链的长波连续模型，通过通量守恒离散化，在约$10^3$网格节点下获得接近$2/5$的有限尺寸热导率指数，为研究非谐系统反常输运提供了实用途径。
AI 中文摘要
通过分子动力学解析对称$\beta$-费米-帕斯塔-乌拉姆-青格链的反常热导率指数，由于长的有限尺寸交叉效应和热接触电阻，可能需要非常大的系统。受此计算挑战的启发，我们推导了一个长波连续介质描述，并研究了动力学理论标度$\kappa\propto L^{2/5}$是否能在适度的数值自由度下实现。非线性弹性场保留了微观相互作用的立方应力，并与朗之万热库交换热量。一个通量守恒的空间离散化从同一应力构造力和能量流，提供了一致的内部输运估计。对于$L>8$，在参考分辨率下对应约$10^3$个网格节点及以上，拟合指数为$0.399\pm0.004$。网格细化支持了该指数在两个更细分辨率之间的稳定性，尽管电导率幅度仍然依赖于分辨率。因此，主要结果是一个接近$2/5$的可访问有限尺寸区域，而不是随着网格间距消失而绝对电导率的收敛。该公式为研究非谐系统中的反常输运提供了一条实用途径，并为研究非线性弹性介质中的能量流提供了一个保守的连续介质框架。
英文摘要
Resolving the anomalous conductivity exponent of the symmetric $β$-Fermi--Pasta--Ulam--Tsingou chain by molecular dynamics can require very large systems because of long finite-size crossovers and thermal-contact resistance. Motivated by this computational challenge, we derive a long-wavelength continuum description and investigate whether the kinetic-theory scaling $κ\propto L^{2/5}$ becomes accessible with a moderate number of numerical degrees of freedom. The nonlinear elastic field retains the cubic stress of the microscopic interaction and exchanges heat with Langevin reservoirs. A flux-conservative spatial discretization constructs the force and energy current from the same stress, providing a consistent interior transport estimator. For $L>8$, corresponding to approximately $10^3$ mesh nodes and above at the reference resolution, the fitted exponent is $0.399\pm0.004$. Mesh refinement supports the stability of this exponent between the two finer resolutions, although the conductivity amplitude remains resolution-dependent. The main result is thus an accessible finite-size regime near $2/5$, rather than convergence of the absolute conductivity as the mesh spacing vanishes. This formulation provides a practical route to studying anomalous transport in anharmonic systems and a conservative continuum framework for investigating energy flow in nonlinear elastic media.
Comments15 pages, 6 figures
