Bulk viscosity of resonating fermions revisited: Kubo formula, sum rule, and the dimer and high-temperature limits

The bulk viscosity of two-component fermions with a zero-range interaction is revisited both in two and three dimensions. We first point out that the “standard” Kubo formula employed in recent studies has flaws to give rise to an unphysical divergent bulk viscosity even in a limit where it is supposed to vanish. The corrected Kubo formula as well as the sum rule is, then, carefully rederived so as to confirm that the bulk viscosity, indeed, vanishes in the free, unitarity, and dimer limits. We also discuss that the recently found discrepancy between the Kubo formalism and the kinetic theory for the bulk viscosity is attributed to the fact that the quasiparticle approximation assumed by the latter breaks down even in the high-temperature limit.

Figure 1

Diagrammatic representation of (top) the pair propagator and (bottom) the contact-contact response function, which become exact both in the dimer limit and in the high-temperature limit. The single and double lines represent the fermion and pair propagators, respectively, whereas the dot is a bare coupling constant, and the square is to insert the contact density operator.

Figure 2

Frequency-dependent complex bulk viscosity $\zeta (\omega +i{0}^{+})$ in the dimer limit for (top) $d=2$ and (bottom) $d=3$ in units of the number density. Its real and imaginary parts are plotted by the solid and dashed curves, respectively, and the frequency is normalized by the binding energy of dimers.

Figure 3

Diagrammatic representation of the fermion self-energy. See the caption of Fig. 1 for the other details.