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arXiv 2003.10338cond-mat.quant-gascond-mat.str-el
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幺正费米气体的量子临界热输运

Quantum critical thermal transport in the unitary Fermi gas

Bernhard Frank, Wilhelm Zwerger, Tilman Enss

摘要:

强关联系统通常与一个潜在的量子临界点相关联,该临界点决定了它们在有限温度相图中的行为。它们的热力学和输运性质来自临界涨落并遵循普遍的标度定律。在这里,我们开发了一个微观理论的热输运在量子临界制度表示的热总和规则和有效的散射时间。我们显式地计算了量子临界模型系统幺正费米气体的特征标度函数。此外,我们推导出一个精确的热和规则的热量和能量流和数值计算使用非微扰Luttinger-Ward方法。对于热散射时间,我们找到一个简单的量子临界标度形式。总的来说,求和规则和散射时间决定了从高温到量子临界状态的热导率、热扩散率、普朗特数和声扩散率。结果提供了一个定量描述最近的超冷费米气体的声衰减测量。

英文摘要:

Strongly correlated systems are often associated with an underlying quantum critical point which governs their behavior in the finite temperature phase diagram. Their thermodynamical and transport properties arise from critical fluctuations and follow universal scaling laws. Here, we develop a microscopic theory of thermal transport in the quantum critical regime expressed in terms of a thermal sum rule and an effective scattering time. We explicitly compute the characteristic scaling functions in a quantum critical model system, the unitary Fermi gas. Moreover, we derive an exact thermal sum rule for heat and energy currents and evaluate it numerically using the nonperturbative Luttinger-Ward approach. For the thermal scattering times we find a simple quantum critical scaling form. Together, the sum rule and the scattering time determine the heat conductivity, thermal diffusivity, Prandtl number and sound diffusivity from high temperatures down into the quantum critical regime. The results provide a quantitative description of recent sound attenuation measurements in ultracold Fermi gases.

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