Some comments on Kondo lattices and the Mott transition

The so called exhaustion problem occurs when few electrons have to screen many spins in a metal with magnetic impurities. A singlet Fermi liquid ground state is possible only if all impurities are "isotropized" in such a way as to suppress their entropy. That takes a time tau(c) and the corresponding Energy epsilon(c) = (h) over bar/tau(c) limits the Fermi liquid range. The present note explores that issue of time and energy scales, and it concludes that epsilon(c) is much smaller than the single impurity Kondo temperature. Similarly the relevant energy scale is proportional to the number of electrons. Recent results on the Mott metal insulator transition in infinite dimension are reconsidered in the light of these results: controversies in that respect are shown to reduce to a simple physical question, with no firm answer as to now.