有限温度洛伦兹数与热导率：铝和碳从常温到百万度开尔文的热导率
The finite-$T$ Lorentz number and the thermal conductivity. Aluminum and carbon conductivities from ambient to millions of degrees Kelvin
AI总结：
本文提出用基本费米积分表示的有限温度洛伦兹数普适形式及其四参数拟合，简化金属型体系热导率计算，并给出铝和碳在百万开尔文范围内的计算结果与实验及模拟对比。
摘要：
如果能够方便地将洛伦兹数 $L_N$ 推广到任意温度（$T$）和密度，金属型电子-离子体系热导率 $κ$ 的理论预测将大大简化。这类计算在天体物理学、高能量密度物理、半导体物理以及材料科学中都是必需的。我们给出了 $L_N(T)$ 的有限温度形式，并用基本费米积分表示。它是 $t=T/E_F$ 的普适函数，其中 $E_F$ 是电子的费米能。对 $L_N(t)$ 在 $t=0-\infty$ 范围内进行方便的四参数拟合，进一步简化了应用。本文还简要讨论了电子-电子相互作用的影响。给出了铝和碳在若干压缩比下并进入百万开尔文范围的 $L_N(t)$ 和热导率 $κ$ 的计算结果。作为比较，使用了铝在熔点以上附近的实验等压热导率，以及由现有密度泛函理论模拟和平均原子计算得到的铝和碳的等容热导率。
英文摘要：
Theoretical prediction of the thermal conductivity $κ$ of metal-like electron-ion systems would be greatly simplified if a convenient generalization of the Lorentz number $L_N$ for arbitrary temperatures ($T$) and densities were available. Such calculations are needed in astrophysics, high-energy-density physics, semiconductor physics as well as in materials science. We present a finite-$T$ form of $L_N(T)$, expressed in terms of elementary Fermi integrals. It is a universal function of $t=T/E_F$, where $E_F$ is the Fermi energy of the electrons. A convenient four-parameter fit to $L_N(t)$ for $t=0-\infty$ further simplifies the applications. The effect of electron-electron interactions is also briefly discussed. Calculations for $L_N(t)$ and thermal conductivities $κ$ for Al and C are presented at several compressions and into the million-Kelvin range. Experimental isobaric conductivities for Al just above the meting point, and isochoric conductivities for Al and C from available density-functional theory simulations and average-atom calculations are used as comparisons.
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