  Background: The two-flavor color superconducting (2SC) phase of quark matter
is a possible constituent of the core of neutron stars. To assess its impact on
the observable behavior of the star one must analyze transport properties,
which in 2SC matter are controlled by the scattering of gapless fermionic modes
by each other and possibly also by color-magnetic flux tubes. Purpose: We
determine the electrical and thermal conductivities and the shear viscosity of
2SC matter. Methods: We use a variational formulation of transport theory,
treating the strong and electromagnetic interactions via a weak coupling
expansion. Results: We provide the leading order scaling of the transport
coefficients with temperature and chemical potential as well as accurate fits
to our numerical results. We also find that the scattering of fermions by
color-magnetic flux tubes is insignificant for thermal conductivity, but may
contribute to the electrical conductivity and shear viscosity in the limit of
very low temperature or high magnetic field. We also estimate the transport
coefficients in unpaired quark matter. Conclusions: Our calculation has set the
stage for exploration of possible signatures of the presence of 2SC quark
matter in neutron stars.
