  We investigate electron transport under the two impurity Kondo problem with
the Aharonov--Bohm and Aharonov--Casher effects. These interference effects
induce the Ising-coupled Ruderman--Kittel--Kasuya--Yosida (RKKY) interaction.
We discuss the inter- and intra-site spin conductance as well as charge
conductance in the Kondo and the mixed-valence regimes using the slave boson
mean field approximation.
