Distributions of Conductance and Shot Noise and Associated Phase Transitions

For a chaotic cavity with two identical leads each supporting $N$ channels, we compute analytically, for large $N$, the full distribution of the conductance and the shot noise power and show that in both cases there is a central Gaussian region flanked on both sides by non-Gaussian tails. The distribution is weakly singular at the junction of Gaussian and non-Gaussian regimes, a direct consequence of two phase transitions in an associated Coulomb gas problem.

Figure 1

Charge density ${\varrho }_p^{\star }(T)$ for conductance (numerical, in red dots; theory, in solid black line). From left to right $p=6$, $-1$, $-6$. The numerical density [14] (details will be published elsewhere) is for $N=5$ and $\beta =2$.

Figure 2

Left: Free energy difference $J_G(p)$ (red) and $J_Q(p)$ (blue) from Monte Carlo (MC) simulations and theory (solid line). We have used $-30\le p\le 30$, $\beta =2$ and $N=5$ (for conductance) and $N=4$ (for shot noise), respectively. Right: Rate functions ${\Psi }_G(x)$ (green) and ${\Psi }_P(x)$ (blue) [see (9, 10)]. The black dots indicate the two critical points on each curve.

Figure 3

Charge density ${\varrho }_p^{\star }(\mu )$ for the shifted shot noise $Q$. From left to right $p=12$, 2, $-10$.