note that the variation of I$_{typ}$ with Δ φ is quite sim- ilar to that as presented in Fig. 3. The typical cur- rent amplitude varies periodically with Δ φ showing view of such a quantum interferometer is given in Fig. 6, where we set N = 15. The vertical line con- necting left and right sub-rings contains 5 atomic sites, where the individual sub-rings are penetrated by AB fluxes φ$_{1}$ and φ$_{2}$ , respectively. In this inter- ferometric geometry, the phase factors ( θ$_{ij}$ ’s) are chosen according to our earlier prescription. Along the circumference of the ring θ$_{ij}$ = 2 πφ/ 12 φ$_{0}$ and along the vertical line θ$_{ij}$ = 2 π Δ φ/ 5 φ$_{0}$ , where φ and Δ φ correspond to the identical meaning as before. GLYPH<Minus> 2 GLYPH<Minus> 1 0 1 2 Φ$_{2}$ 0 1 2 I typ GLYPH<LParen1> b GLYPH<RParen1> GLYPH<Minus> 2 GLYPH<Minus> 1 0 1 2 Φ$_{2}$ 0 1 2 I typ GLYPH<LParen1> a GLYPH<RParen1> Drain Source Quantum Interferometer 1 2 Figure 6: (Color online). Schematic view of a quantum interferometer with 15 atomic sites ( N = 15) attached to two semi-infinite one-dimensional metallic electrodes. Figure 5: (Color online). I$_{typ}$ - φ$_{2}$ curves in the weak- (black) and strong-coupling (red) limits for the in- terferometer with four atomic sites ( N = 4), where (a) φ$_{1}$ = 0 and (b) φ$_{1}$ = 0 . 3. The typical cur- rent amplitudes are calculated at the bias voltage V = 1 . 02. 2 φ$_{0}$ flux-quantum periodicity, following the g$_{typ}$ -Δ φ characteristics. For this bigger quantum interferometer ( N = 15), exactly similar features of conductance-energy and current-voltage characteristics are observed as we see in the case of a 4-site interferometer. Also, typ- ical current amplitude I$_{typ}$ shows identical variation with φ$_{2}$ to our previous study. Only the typical con- ductance g$_{typ}$ varies in a different way as a function of Δ φ . As illustrative examples in Fig. 7 we plot g$_{typ}$ -Δ φ characteristics for the quantum interferom- eter with N = 15 in the limit of strong-coupling, where (a) and (b) correspond to φ = 0 . 4 and 0 . 8, respectively. The typical conductances are deter- mined at the energy E = 1 . 5. From the spectra we notice that for a fixed value of φ , typical con- ductance oscillates as a function of Δ φ exhibiting 5 φ$_{0}$ flux-quantum periodicity. This phenomenon is completely different from the traditional periodic nature. Comparing the results presented in Figs. 3 and 7 it is manifested that the periodicity of g$_{typ}$ - Δ φ curves depends on the total number of atomic With the above description of electron transport for a 4-site ( N = 4) quantum interferometer, now we can extend our discussion for an interferometer with higher number of atomic sites i.e., N > 4. To get an experimentally realizable system, here we consider a quantum interferometer with large num- ber of atomic sites compared to our presented math- ematical model with 4 atomic sites. The schematic 8 3.2 Interferometric geometry with N atomic ( $^{N >}$4 ) sites