Dynamic renormalization group (RG) of fluctuating viscoelastic equations is investigated to clarify the cause for numerically reported disappearance of anomalous heat conduction (recovery of Fourier's law) in low-dimensional momentum-conserving systems. RG flow is obtained explicitly for simplified two model cases: a one-dimensional continuous medium under low pressure and incompressible viscoelastic medium of arbitrary dimensions. Analyses of these clarify that the inviscid fixed point of contributing the anomalous heat conduction becomes unstable under the RG flow of nonzero elastic-wave speeds. The dynamic RG analysis further predicts a universal scaling of describing the crossover between the growth and saturation of observed heat conductivity, which is confirmed through the numerical experiments of Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) lattices.

中文翻译：

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动量守恒下低维固体中傅立叶定律恢复的通用标度。

研究了波动粘弹性方程的动态重归一化组（RG），以澄清低维动量守恒系统中数值传热异常传导消失（傅立叶定律的恢复）的原因。对于简化的两种模型情况，可以显式获得RG流：低压下的一维连续介质和任意尺寸的不可压缩粘弹性介质。这些分析表明，在非零弹性波速的RG流动下，导致异常热传导的无形固定点变得不稳定。动态RG分析进一步预测了描述观察到的热导率的增长和饱和之间的交叉的通用比例，这已通过费米-帕斯塔-乌拉姆的数值实验得到了证实$\beta$ （FPU-$\beta$）格。