GLYPH<Minus> 4 GLYPH<Minus> 2 0 2 4 GLYPH<CapDelta>Φ 0 1 2 g typ GLYPH<LParen1> d GLYPH<RParen1> GLYPH<Minus> 4 GLYPH<Minus> 2 0 2 4 GLYPH<CapDelta>Φ 0 1 2 g typ GLYPH<LParen1> c GLYPH<RParen1> GLYPH<Minus> 4 GLYPH<Minus> 2 0 2 4 GLYPH<CapDelta>Φ 0 1 2 g typ GLYPH<LParen1> b GLYPH<RParen1> GLYPH<Minus> 4 GLYPH<Minus> 2 0 2 4 GLYPH<CapDelta>Φ 0 1 2 g typ GLYPH<LParen1> a GLYPH<RParen1> Figure 3: (Color online). g$_{typ}$ -Δ φ curves in the strong-coupling limit for the interferometer with four atomic sites ( N = 4), where (a) φ = 0 . 2, (b) φ = 0 . 4, (c) φ = 0 . 6 and (d) φ = 0 . 8. The typical conductances are calculated at the energy E = 5. A clear investigation shows that the positions of the anti-resonances on the energy scale are inde- pendent of the interferometer-to-electrode coupling strength. Since the width of these anti-resonance states are too small, they do not provide any sig- nificant contribution in the current-voltage ( I - V ) characteristics. The effect of Δ φ , the difference between two AB fluxes φ$_{1}$ and φ$_{2}$ , on the electron transport through function of Δ φ for the interferometer in the limit of strong-coupling. Figures 3(a), (b), (c) and (d) cor- respond to the results for φ = 0 . 2, 0 . 4, 0 . 6 and 0 . 8, respectively. The typical conductances are calcu- lated for the fixed energy E = 5. Very interestingly we observe that, for a fixed value of φ , typical con- ductance varies periodically with Δ φ showing 2 φ$_{0}$ (= 2, since φ$_{0}$ = 1 in our chosen unit) flux-quantum periodicity, associated with the number of atomic sites (2) in the vertical line connecting two sub- rings of the quantum interferometer. This period doubling behavior is completely different from the traditional periodic nature, since in conventional ge- ometries we get simple φ$_{0}$ flux-quantum periodicity. In the limit of weak-coupling we will also get the similar behavior of periodicity (2 φ$_{0}$ ) for the typical conductance with Δ φ , and due to the obvious rea- son we do not plot the results for this coupling limit once gain. 3.1.2 Typical conductance g$_{typ}$ as a function of Δ φ 3.1.3 Current-voltage characteristics the interferometer is also an important issue in the present context. To visualize it, in Fig. 3, we display the variation of the typical conductance ( g$_{typ}$ ) as a 6 All these features of electron transfer become much more clearly visible by studying the current- voltage ( I - V ) characteristics. The current I pass- ing through the interferometer is computed from the integration procedure of the transmission func- tion T as prescribed in Eq. (6) which is not re- stricted in the linear response regime, but it is of great significance in determining the shape of the full current-voltage characteristics. As illustrative examples, in Fig. 4, we plot the current-voltage characteristics of the interferometer for the three different values of φ$_{2}$ , keeping the flux φ$_{1}$ in the left sub-ring to a fixed value 0 . 2. The red, blue and black curves correspond to φ$_{2}$ = 0, 0 . 1 and 0 . 4, respectively. In the limit of weak-coupling (see Fig. 4(a)), it is observed that the current exhibits staircase-like structure with fine steps as a function of the applied bias voltage V . This is due to the existence of the sharp resonant peaks in the con- ductance spectrum in this coupling limit, since the current is computed by the integration method of