V + eff. and V − eff. represent the opposite voltage drop on each side of the wire which, due to the symmetry h(x,d) = h(-x,d) obeys, V + eff. + V − eff. = 0. In the present case, due to the symmetry, we can not observe the voltage n$_{e}$ ( v $_{v$_{eff.}$}$)( πe κ ) W [ L $_{d}$, ξ $_{a}$]. We believe that for an asymmetric situation this voltage might be measured. For the case where half of the wire-leads system x ≥ d 2 is controlled by the strong interaction U = ∞ and the other half x < d 2 is non-interacting U = 0, the conductance will be affected by the voltage V + $_{eff.}$. This voltage is in the range of 10 − $^{9}$volts and might be measurable. In figure 3 we show the potential W [ L $_{d}$, ξ $_{a}$] as a function of the screening length. Equation (38) shows that the conductance for d L$_{T,L}$ = 1 is given by G = 2(0 . 5 e 2 h ), reflecting the fact that the anomalous commutator for the wire has been modified to i $_{2}$¯ h . For different lengths the conductance is modified. Following [21], we investigate the dependence of the conductance in terms of L D and d L$_{T}$ (the effect of the overlapping region ϵ between the leads and the wire studied by [21] will be neglected here). The thermal length L$_{T}$ ≡ ¯ hv$_{eff.}$ K$_{B}$T = v$_{eff.}$ v ¯ hv K$_{B}$T = (1 − 3 d 4 $_{L}$) L (0) T where L (0) T is the thermal length defined in the leads . The length L$_{T,L}$ ≈ L$_{T}$ ≤ L is given by the crossover function: 1 L$_{T,L}$ ≈ 1 L$_{T}$ [1 + L$_{T}$ L ]. As a result we find for the conductance: The result, of equation (40) is shown in figure 2. We observe that when the length of the wire d = ¯ hv K$_{B}$T$_{d}$ is in the range T$_{d}$ T ≈ 1 − 2 the conductance is anomalous in agreement with the experimental results reported in ref. [24]. (In the experiments the anomalous conductance is obtained as a result of the variation of the gate voltage, we will interpret this result as the region where the strong coupling point U = ∞ has been reached. At this point, when the temperature or the length are varied the conductance varies. We believe that this variation of the conductance is demonstrated in figure 2.) 17 G [ d L , T$_{d}$ T ; U = ∞ ] = (2 e 2 h )[1 − 1 2 T T$_{d}$ 1 (1 − 3 4 d $_{L}$) (1 + ( T$_{d}$ T )( d L )(1 − 3 4 d L ))] (40) V (+) eff. = − V ( − ) eff. = n$_{e}$ ( v v$_{eff.}$ )( πe κ ) ∫ L T,L 2 0 dx (1 − h(x,d) 2 ) $^{2}$[ ∫ L 2 − L 2 dy 1 2 ∂$_{x}$ [ h(y,d) √ ( x − y ) 2 + a 2 − h(y,d) √ ( x − y ) 2 + ξ $_{2}$] ≡ n$_{e}$ ( v v$_{eff.}$ )( πe κ ) W [ L d , ξ a ] (39)