content_image/333002.jpg content_image/333001.jpg content_image/333003.jpg content_image/333004.jpg
most symmetrically possible situation M$_{L}$ = M$_{R}$ ± 1, but the conclusions of the present paper are not qualitatively affected by this choice. 

For one-dimensional models with nearest-neighbor hopping (the class to which the above model belongs), the contact “surfaces” between the extended molecule and the left and right electrodes reduce to two points, which are located at − M$_{L}$ and + M$_{R}$ , respectively. Therefore, the self-energies Σ r 0 ,L and Σ r 0 ,R needed to calculate the current of Eq. (16) possess a single nonvanishing elements, namely ( Σ r 0 ,L ) − M$_{L}$, − M$_{L}$ ≡ Σ$_{L}$ and ( Σ r 0 ,R ) M$_{R}$,M$_{R}$ ≡ Σ$_{R}$. For model (19), Σ r $_{x}$( ε ) = β 2 $_{x}$g r $_{x}$( ε ) where g r x is the retarded Green’s function at the ends of 

semi-infinite electrodes coupled to the extended molecule. By using the expression of g r $_{x}$( ε ) [27], one straightforwardly obtains 

<img src='content_image/333002.jpg'>

<img src='content_image/333001.jpg'>

where θ is the step (Heaviside) function. The above expressions, along with the Dyson equation for the retarded Green’s function deduced from Eq. (14) 

<img src='content_image/333003.jpg'>

complete the formulae needed to compute the current (16). 

## V. NUMERICAL RESULTS FOR THE LINEAR CONDUCTANCE 

We note that, although Eq. (16) as well as the subsequent equations for the nonequi- librium Green’s functions are valid for an arbitrary voltage, in the presentation of the nu- merical results of this section we shall restrict ourselves to the case of linear conductance G ≡ dI/dV |$_{V}$ =0 . For completeness, we give its expression for the case of a sufficiently large extended molecule, which can be obtained by taking µ$_{L,R}$ = ε$_{F}$ ± eV / 2 and V → 0 in Eq. (16) 

<img src='content_image/333004.jpg'>

where G 0 ≡ e $^{2}$/h is the conductance quantum. For the sake of simplicity, we shall suppose that the electrodes are identical and therefore ξ$_{L}$ = ξ$_{R}$ ≡ ξ , β$_{L}$ = β$_{R}$ ≡ β , Γ$_{L}$( ε$_{F}$ ) = Γ$_{R}$( ε$_{F}$ ) = 2 β $^{2}$/ξ ≡ Γ, and J$_{L}$ = J$_{R}$ ≡ J . Unlike in most of the studies on the IRLM or 

