14 research outputs found
Viscosity Sum Rules at Large Scattering Lengths
We use the operator product expansion (OPE) and dispersion relations to
obtain new model-independent "Borel-resummed" sum rules for both shear and bulk
viscosity of many-body systems of spin-1/2 fermions with predominantly short
range S-wave interactions. These sum rules relate Gaussian weights of the
frequency-dependent viscosities to the Tan contact parameter C(a). Our results
are valid for arbitrary values of the scattering length a, but receive small
corrections from operators of dimension larger than 5 in the OPE, and can be
used to study transport properties in the vicinity of the infinite scattering
length fixed point. In particular, we find that the exact dependence of the
shear viscosity sum rule on scattering length is controlled by the function
C(a). The sum rules that we obtain depend on a frequency scale w that can be
optimized to maximize their overlap with low-energy data