text: We now perform the same calculations in the presence 
  of lattice dispersion. The results are summarized in Figs 
  4,5, and 6. 
  ω 
  (ω + iδ)2 − ∆2 
  (12) 
  
  Fig 4 shows conductivities σ(ω) in the NS and the SCS 
  and Kubo sums WK plotted against impurity scattering 
  Γ. We see that the optical integral in the NS is always 
  greater than in the SCS. The negative sign of ∆WK is 
  simply the consequence of the fact that nk is larger in the 
  NS for ǫk < 0 and smaller for ǫk < 0, and ∇2ε~k closely 
  follows −ε~k for our choice of dispersion38), Hence nk is 
  larger in the NS for ∇2ε~k > 0 and smaller for ∇2ε~k < 
  0 and the Kubo sum rule, which is the integral of the 
  product of nk and ∇2ε~k (Eq. 3), is larger in the normal 
  state. 
  
  We also see from Fig. 4 that ∆WK decreases with Γ 
  reﬂecting the fact that with too much impurity scattering 
  there is little diﬀerence in nk between NS and SCS. 