7 We now increase further the number of attached leads. 47 In Figs. 7(a), 8(a), and 9(a) we plot the aver- age conductance 〈 T 〉 , the variance of the conductance var( T ), and the shot noise power P for the non-periodic version of the PBRM model for several values of b with M ∈ [1 , 5]. 48 It is clear from these three plots that chang- ing b from small ( b ≪ 1) to large ( b > 1) values produces a transition from localized- to delocalized-like behavior in the scattering properties of the PBRM model. That is, (i) for b < 0 . 1, 〈 T 〉 ≈ 0, var( T ) ≈ 0, and P ≈ 0; and (ii) for b ≥ 10, 〈 T 〉 , var( T ), and P are well described by the corresponding RMT predictions given by Eqs. (10), (11), and (12), respectively. Similar plots are obtained (not shown here) for the periodic PBRM model. Moreover, we have observed that 〈 T 〉 , var( T ), and P behave (for all M ) as 〈 | S$_{12}$ | $^{2}$〉 b does. See Eq. (14). Thus, we can write where X represents 〈 T 〉 , var( T ), or P and δ is a fitting parameter. Then, in Figs. 7(b), 8(b), and 9(b) we plot 〈 T 〉 , var( T ), and P normalized to their respective COE Since the most prominent realization of systems that undergo a MIT is the 3D Anderson model, it is of rele- vance to analyse its scattering and transport properties average values, now for the periodic PBRM model as a function of bδ for M ∈ [1 , 5]. Also, similar plots are obtained (not shown here) for the non-periodic PBRM model. C. Mean and variance of the conductance and the shot noise power FIG. 8: (Color online) (a) Variance of T as a function of M for the non-periodic PBRM model at criticality for several values of b . var( T ) for the 3D Anderson model at criticality (3DAM) is also shown. (b) var( T ) / var( T ) COE as a function of bδ for the periodic PBRM model at criticality for M ∈ [1 , 5]. Insert: δ versus M . δ is obtained from the fitting of Eq. (24) to the var( T ) vs. b data. Thick full lines correspond to var( T ) = 0. Blue (gray) dashed lines are (a) the RMT prediction for var( T ) given by Eq. (11); and (b) one. FIG. 9: (Color online) (a) Shot noise power P as a function of M for the non-periodic PBRM model at criticality for sev- eral values of b . P for the 3D Anderson model at criticality (3DAM) is also shown. (b) P/P COE as a function of bδ for the periodic PBRM model at criticality for M ∈ [1 , 5]. Insert: δ versus M . δ is obtained from the fitting of Eq. (24) to the P vs. b data. Thick full lines correspond to P = 0. Blue (gray) dashed lines are (a) the RMT prediction for P given by Eq. (12); and (b) one. FIG. 10: Probability distribution ρ (ln T ) for the 3D Anderson model at criticality in the cases M = 1 and M = 2. Dashed lines with slopes T 1 / 2 and T 2 are plotted to guide the eye. III. 3D ANDERSON MODEL X ( b ) = X COE [ 1 1 + ( δb ) − 2 ] , (24) 1 2 3 4 5 M 0 0.05 0.1 var(T) b = 0.02 b = 0.04 b = 0.1 b = 0.2 b = 0.4 b = 1 b = 4 b = 10 3DAM 0.01 0.1 1 10 b 0 0.5 1 var(T)/var(T) COE M = 1 M = 2 M = 3 M = 4 M = 5 1 2 3 4 5 M 2.5 3 3.5 (a) (b) 1 2 3 4 5 M 0 0.3 0.6 P b = 0.02 b = 0.04 b = 0.1 b = 0.2 b = 0.4 b = 1 b = 2 b = 10 3DAM 0.01 0.1 1 10 b 0 0.5 1 P/P COE M = 1 M = 2 M = 3 M = 4 M = 5 1 2 3 4 5 M 2 3 4 (b) (a) -15 -10 -5 0 ln T 10 -4 10 -3 10 -2 10 -1 (ln T) ~ T 1/2 ~ T 2 M = 1 M = 2