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 contributions 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 length we derive the complete bulk viscosity at second order in fugacity and show that part of this result can be calculated from a kinetic equation. For positive scattering length a new type of pinch singularity arises for bound pairs. We derive a novel kinetic equation for bound pairs from the self-consistent equation for the vertex function and show that the bulk viscosity at positive scattering length has contributions at first order in fugacity, one order lower than at negative scattering length, because of the pinch singularity for bound pairs.

K. Fujii, T. Enss, “Bulk viscosity of resonantly interacting fermions in the quantum virial expansion”,  arXiv:2208.03353 (2022).


Related to Project C02, C03