Department of Physics, Fuzhou University, Fuzhou 350108, Fujian, China.
Phys Rev E. 2018 Feb;97(2-1):022116. doi: 10.1103/PhysRevE.97.022116.
We address the issue of whether the golden-mean [ψ=(sqrt[5]+1)/2≃1.618] universality class, as predicted by several theoretical models, can be observed in the dynamical scaling of thermal transport. Remarkably, we show strong evidence that ψ appears to be the scaling exponent of heat mode correlation in a purely quartic anharmonic chain. This observation seems to somewhat deviate from the previous expectation and we explain it by the unusual slow decay of the cross correlation between heat and sound modes. Whenever the cubic anharmonicity is included, this cross correlation gradually dies out and another universality class with scaling exponent γ=5/3, as commonly predicted by theories, seems recovered. However, this recovery is accompanied by two interesting phase transition processes characterized by a change of symmetry of the potential and a clear variation of the dynamic structure factor, respectively. Due to these transitions, an additional exponent close to γ≃1.580 emerges. All this evidence suggests that, to gain a full prediction of the scaling of thermal transport, more ingredients should be taken into account.
我们研究了在热输运的动力标度中是否可以观察到几个理论模型所预测的黄金均值 [ψ=（sqrt[5]+1）/2≃1.618] 普遍性类。值得注意的是，我们有力地证明了 ψ 似乎是纯四次非谐链中热模相关的标度指数。这一观察结果似乎与之前的预期有些偏离，我们通过热模和声音模之间的交叉相关的异常缓慢衰减来解释它。只要包含三次非谐性，这种交叉相关就会逐渐消失，并且通常由理论预测的具有标度指数 γ=5/3 的另一个普遍性类似乎会恢复。然而，这种恢复伴随着两个有趣的相变过程，分别以势的对称变化和动态结构因子的明显变化为特征。由于这些转变，出现了一个接近 γ≃1.580 的额外指数。所有这些证据表明，要充分预测热输运的标度，需要考虑更多的因素。
