  We calculate the Kadowaki-Woods ratio (KWR) in Fermi liquids with arbitrary
band structures. We find that, contrary to the single band case, the ratio is
not generally independent of the effects of electronic correlations
(universal). This is very surprising given the experimental findings of a near
universal KWR in many multiband metals. We identify a limit where the
universality of the ratio, which has been observed experimentally in many
strongly correlated electron systems, is recovered. We discuss the KWR in Dirac
semimetals in two and three dimensions. In the two-dimensional case we also
generalize the KWR to account for the logarithmic factor in the self-energy. In
both cases we find that the KWR is independent of correlations, but strongly
dependent on the doping of the system: for massless fermions the KWR is
proportional to the inverse square of the carrier density, whereas the KWR for
systems with massive quasiparticles is proportional to the inverse of the
carrier density.
