It is expected that the energy-diffusion propagator in a one-dimensional nonlinear lattice with three conserved quantities: energy, momentum, and stretch, consists of a central heat mode and two sound modes. The heat mode follows a Lévy distribution. Consequently, the heat diffusion is super, i.e., the second moment of the diffusion propagator diverges as $t^{\beta }$ with $\beta >1$; and the heat conduction is anomalous, i.e., the heat conductivity is size dependent and diverges with size $N$ by $N^{\alpha }$, with $\alpha >0$. In this paper, we study a one-dimensional lattice with two-dimensional transverse motions, in which the total angular momentum also conserves. More importantly, the diffusion of this conserved quantity is ballistic. Surprisingly, the above pictures and the values of the mentioned power exponents keep unchanged. The universality of the scalings is then further extended. On the other hand, the detailed strengths of heat transports are largely enhanced. Such a counterintuitive finding can be explained by the change of the phonon mean-free path of the lattices.

中文翻译：

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角动量守恒晶格中的热传输

预计一维非线性晶格中的能量扩散传播器具有三个守恒量：能量、动量和拉伸，由一个中心热模式和两个声音模式组成。热模式遵循 Lévy 分布。因此，热扩散是超的，即扩散传播器的二阶矩发散为$t^{\beta }$和$\beta >1$; 并且热传导是反常的，即热导率与尺寸相关并且随尺寸而变化$氮$经过${氮}^{\alpha }$， 和$\alpha >0$。在本文中，我们研究了具有二维横向运动的一维晶格，其中总角动量也守恒。更重要的是，这个守恒量的扩散是弹道式的。令人惊讶的是，上面的图片和提到的幂指数的值保持不变。然后进一步扩展了标度的普遍性。另一方面，热传输的细节强度大大增强。这种违反直觉的发现可以通过晶格声子平均自由程的变化来解释。