Figure 1

Conductance distributions for bulk disordered wires. $\beta =1$ ($\beta =2$) indicates the presence (absence) of time-reversal symmetry. Continuous lines correspond to $P(g)$ obtained from the Monte Carlo solution of the DMPK equation with $N=6$. Results for surface disordered wires are shown for comparison (after Ref. 10). Symbols represent the numerical calculations based on the Anderson model for different configurations. For $\beta =2$, the calculations are performed at half band ($E_F=0$), disorder strength $W=2$, and different values of $[N,\varphi ]$: $[7,0.05;\circ ]$, $[7,0.1;\square ]$, $[5,0.05;▿]$, $[5,0.1;△]$, $[3,0.05;◃]$, and $[3,0.1;▹]$; for $\beta =1$, the results correspond to different values of $[N,E_F,W]$: $[7,0,2;\circ ]$, $[10,0,2;\square ]$, $[3,0,2;▿]$, $[5,0,2;△]$, $[7,0,1.5;◃]$, $[7,0,4;▹]$, $[7,-0.9,2;\diamond ]$, and $[7,-2.3,2;\star ]$. Selected $⟨g⟩$ values were obtained from the appropiate values of $L$ (Anderson) and $s$ (DMPK) for the different cases [20].Reuse & Permissions

Figure 2

DMPK results for the first conductance cumulants: variance (a), skewness (b), and kurtosis (c) versus the average conductance $⟨g⟩$ for $N=20$ and both $\beta =1$ (open squares) and 2 (open circles). Numerical results for different channels $N=2,3,4,5,6$ are shown in (a) as dashed lines. Thick continuous lines correspond to the expected leading corrections obtained from perturbation theory (after Ref. 15). (d) Averaged transmission eigenvalues $⟨T_i⟩$ as a function of $⟨g⟩$ for $N=20$ and both $\beta =1$ (continuous line) and 2 (discontinuous line). Vertical lines define different regions where the statistics is governed by one and two channels.Reuse & Permissions