Quasi-particle description for the transport through a small interacting system

We study effects of electron correlation on the transport through a small interacting system connected to reservoirs using an effective Hamiltonian which describes the free quasi-particles of a Fermi liquid. The effective Hamiltonian is defined microscopically with the value of the self-energy at $\omega=0$. Specifically, we apply the method to a Hubbard chain of finite size $N$ ($=1, 2, 3, ...$), and calculate the self-energy within the second order in $U$ in the electron-hole symmetric case. When the couplings between the chain and the reservoirs on the left and right are small, the conductance for even $N$ decreases with increasing $N$ showing a tendency toward a Mott-Hubbard insulator. This is caused by the off-diagonal element of the self-energy, and this behavior is qualitatively different from that in the special case examined in the previous work. We also study the effects of the asymmetry in the two couplings. While the perfect transmission due to the Kondo resonance occurs for any odd $N$ in the symmetric coupling, the conductance for odd $N$ decreases with increasing $N$ in the case of the asymmetric coupling.