Distribution of the Kondo Temperature in Mesoscopic Disordered Metals

The Kondo temperature of a magnetic impurity in a weakly disordered metal is distributed due to the randomness in the local exchange coupling, and the local electronic density of states (LDOS). We show that in a closed, phase coherent metal particle the resulting distribution of $T_K$ is strongly asymmetric and scales with the mean level spacing $\Delta$. Its width is $2 \sqrt{\Delta/\beta T_K}$, where $\Delta$ is the mean level spacing, and $\beta=1,2$, with, without time reversal symmetry, respectively. Increasing the density of magnetic impurities, the distribution of Kondo temperatures (DKT) is found to become more narrow. Corrections to these results due to Anderson localisation are discussed.