Resolution:
## Figure 2.
Schematic drawing of the density of states in the lead for the reduced model, in situations
(a) . The half of band width is L_{c }≪ L_{K }≪ L, (b) L_{c }≪ L ≪ L_{K}, and (c) L ≪ L_{c }≪ L_{K}, where L is the size of the AB ring, L_{c }is the screening length of charge fluctuation, and L_{K }is that of spin fluctuation, i.e., size of Kondo screening cloudD_{1 }≃ |ε_{0}| in the second stage of scaling. In situation (a), ε_{T }≪ T_{K }≪ |ε_{0}|. The oscillating part of ν(ε) is averaged out in the integration of scaling equations. In consequence, the Kondo
temperature _{k}T_{K }does not depend on the ring size nor AB phase ϕ of the magnetic flux penetrating the ring. In situation (b), T_{K }≪ ε_{T }≪ |ε_{0}|. Then the Thouless energy ε_{T }acts as the high energy cut off. ϕ-dependence of T_{K }is determined by the ratio of ε_{T }to T_{K}. In situation (c), T_{K }≪ |ε_{0}| ≪ ε_{T}. The density of states is almost constant. In this case, T_{K }reflects the density of states at the Fermi level, ν(0).
Yoshii and Eto |