ure). This plot shows that the Kubo sums are almost
completely recovered by integrating up to the bandwidth
of 1eV : the recovery is 95% in the clean limit and ∼ 90%
in the dirty limit. In Fig 6 we plot ∆ W (ωc) as a function
of ωc in clean and dirty limits. ∆ W (∞) is now non-zero,
in agreement with Fig. 4 and we also see that there is