content_image/414698.jpg content_image/414697.jpg content_image/414699.jpg content_image/414700.jpg
<img src='content_image/414698.jpg'>

## C. Mean and variance of the conductance and the shot noise power 

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 

<img src='content_image/414697.jpg'>

<img src='content_image/414699.jpg'>

<img src='content_image/414700.jpg'>

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. 

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 

## III. 3D ANDERSON MODEL 

