Thermal conductance has emerged as a powerful probe of topological order in the quantum Hall effect and beyond. The interpretation of experiments crucially depends on the ratio of the sample size and the equilibration length, on which energy exchange among contrapropagating chiral modes becomes significant. We show that at low temperatures the equilibration length diverges as $1/T^2$ for almost all Abelian and non-Abelian topological orders. A faster $1/T^4$ divergence is present on the edges of the non-Abelian PH-Pfaffian and negative-flux Read-Rezayi liquids. We address experimental consequences of the $1/T^2$ and $1/T^4$ laws in a sample, shorter than the equilibration length.

中文翻译：

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拓扑液体边缘的热平衡。

热导已经成为量子霍尔效应及其以外的拓扑有序的有力探针。对实验的解释至关重要地取决于样品量与平衡长度的比值，对向传播的手性模式之间的能量交换变得十分重要。我们表明，在低温下，平衡长度发散为$\mathrm{1个}/{Ť}^2$适用于几乎所有阿贝尔和非阿贝尔拓扑顺序。更快$\mathrm{1个}/{Ť}^4$非阿贝尔PH-Pfaffian和负通量Read-Rezayi液体的边缘存在发散。我们解决了$\mathrm{1个}/{Ť}^2$ 和 $\mathrm{1个}/{Ť}^4$ 样本中的定​​律，比平衡长度短。