  The quantum interference effect among coupled identical quantum dots is
studied in the present paper in the limit of strong intra-dot Coulomb
interaction. When the average electron number in each dot is a fraction of an
integer, quantum interference effect is greatly enhanced because of the sharing
of extra electrons by multiple dots. We show that if the extra electron (hole)
number is one, the low energy effective Hamiltonian can be map into the
2-channel SU(M) Coqblin-Schriffer model, where M is the total dot number. In
particular, for two-dot system with odd number of total electrons, the model is
equivalent to a two channel Kondo problem with anisotropic coupling between
local spin and conduction bands. The more general situation with (arbitrary)
fractional average electron number in each dot is also discussed. To study the
Kondo effect, we apply the self consistent ladder approximation(SCLA) to study
the electron spectral function for the two-dot system. Similar method is also
used to study the triple-dot system where we show how quantum coherence
manifest itself in the Aharonov-Bohm (AB) effect.
