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N = 3 and N = 4 electrons are outside the bias win- dow and cannot produce steady currents. When the in- teraction strength is further increased to U = 0 . 5 and U = 1 the steady state currents are gradually restored. This could look surprising, but one can see in Fig.1 that by increasing U the ground state configuration with 3 electrons approaches and enters the bias window. Con- sequently the transport becomes again possible. Note that while the steady state currents are not monotonous w.r.t. U the charge absorbed in the system continuously decreases, Fig. 2(b). 

In transport experiments the strength of the electron- electron interaction is indeed fixed. The usual way to obtain the Coulomb blockade is to vary the chemical po- tentials of the leads relatively to the energy levels of the sample, or vice versa. In Fig. 3 we show the currents in both leads for different values of the chemical poten- tial µ$_{R}$ , while keeping fixed µ$_{L}$ = 7. The strength of the Coulomb interaction is U = 1 and µ (0) 4 almost equals µ$_{L}$ . The steady state value of the current decreases as µ$_{R}$ increases, because fewer states are included in the bias window. The Coulomb blockade onset occurs for µ$_{R}$ > 5, when µ (0) 3 drops below µ$_{R}$ . We observe that the 

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maximum value of the total current in the left lead does not change much when µ$_{R}$ varies. In contrast, the tran- sient current in the right lead is negative and increases in magnitude as µ$_{R}$ increases. This means that the right lead feeds the many-body configurations that fall below µ$_{R}$ . 

The contribution of the excited states to the transient and steady state currents depends strongly on the bias window. In Fig. 4 we show the currents entering the sam- ple from the left lead, carried by the states with N = 2 and N = 3 electrons, for µ$_{R}$ = 3 , 4 , 5 (the cases with non- vanishing current in the steady state). We also show sep- arately the contribution to the currents associated to the ground state configurations, related to µ (0) 2 and µ (0) 3 , and the complementary contribution of all the excited states with 2 and 3 particles. In this case the wave vectors of the ground states are mostly given by the non-interacting wave vectors: | 11000 〉 with weight 97% and | 11100 〉 with 98% for N = 2 and N = 3 respectively. 

For µ$_{R}$ = 3 the steady state current of the ground state configuration is vanishingly small and so the total negative current associated to two-particle states comes mostly from the excited states. In the many-body energy spectrum of the isolated sample we obtain 5 excited con- figurations with µ ( i ) 2 ∈ [ µ$_{R}$, µ$_{L}$ ] = [3 , 7]. As µ$_{R}$ moves up the steady state current of the ground state with N = 2 becomes also negative. The combined contributions of the excited states vanishes at µ$_{R}$ = 5. As can be seen from Fig. 1 µ$_{R}$ = 5 is well above µ (0) 2 , but very close to µ (0) 3 . Consequently, the ground configuration with N = 2 is heavily populated in the steady state, whereas the ex- cited states have low probability and thus weak current. Actually, as we have checked, all the currents associated to each excited state with N = 2 vanish individually. In the transient regime however the N = 2 currents in all three cases are dominated by the excites states. 

The currents of the excited states having N = 3 elec- 

