量子维里展开中共振相互作用费米子的体粘滞
Bulk viscosity of resonantly interacting fermions in the quantum virial expansion
AI总结：
本文在量子维里展开框架下计算二维和三维零程相互作用两组分费米子的高温体粘滞，通过处理久保公式零频极限中的挤压奇异性并重求和顶点修正，分别对负、正散射长度给出二阶和一阶结果，并为束缚对提出新的动力学方程。
摘要：
我们考虑在二维和三维中具有零程相互作用的两组分费米子，并计算高温区域任意散射长度下的体粘滞。我们利用逸度的展开来计算体粘滞的久保公式，逸度在高温下充当一个小参数。在久保公式的零频率极限中，会出现挤压奇异性，它们将逸度的阶数降低一阶。这些奇异性可以将非零频率下的高阶顶点修正转变为零频率下的主导阶，因此所有这些贡献都必须被重求和。我们通过考虑这些挤压奇异性，给出了高温区域体粘滞的精确微观计算。对于负散射长度，我们推导出逸度二阶下的完整体粘滞，并证明用于重求和顶点修正的自洽方程等同于一个线性化动力学方程。对于正散射长度，束缚对会出现一种新型挤压奇异性。我们证明束缚对的挤压奇异性导致体粘滞的一阶贡献，这比负散射长度的情况低一阶，并且顶点修正也提供一阶贡献。我们提出了一个由重求和顶点修正的自洽方程导出的束缚对的新动力学方程。
英文摘要：
We consider two-component fermions with a zero-range interaction both in two and three dimensions and calculate the bulk viscosity for an arbitrary scattering length in the high-temperature regime. We evaluate the Kubo formula for the bulk viscosity using an expansion with respect to the fugacity, which acts as a small parameter at high temperatures. In the zero-frequency limit of the Kubo formula, pinch singularities emerge that reduce the order of the fugacity by one. These singularities can turn higher-order vertex corrections at nonzero frequencies into the leading order at zero frequency, so that all such contributions have to be resummed. We present an exact microscopic computation for the bulk viscosity in the high-temperature regime by taking into account these pinch singularities. For negative scattering lengths, we derive the complete bulk viscosity at second order in fugacity and show that a self-consistent equation to resum the vertex corrections is identical to a linearized kinetic equation. For positive scattering lengths, a new type of pinch singularity arises for bound pairs. We show that the pinch singularity for bound pairs leads to a first-order contribution to the bulk viscosity, which is one order lower than that for negative scattering lengths, and that the vertex corrections also provide first-order contributions. We propose a new kinetic equation for bound pairs that derives from a self-consistent equation to resum the vertex corrections.
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