Noiseless scattering states in a chaotic cavity

TL;DR

This paper investigates the transition from quantum to classical transport in a chaotic cavity, revealing the formation of noiseless transmission channels and their impact on shot noise suppression, which can distinguish different scattering mechanisms.

Contribution

It explicitly constructs fully transmitted and reflected scattering states and predicts a nonlinear noise suppression dependent on contact and system parameters.

Findings

Fully transmitted states do not exist for N less than approximately sqrt(k_F L).

Noise is suppressed for N greater than approximately sqrt(k_F L), with a specific dependence on system parameters.

The nonlinear contact dependence of noise can differentiate ballistic chaotic scattering from impurity scattering.

Abstract

Shot noise in a chaotic cavity (Lyapunov exponent $\lambda$, level spacing $\delta$, linear dimension $L$), coupled by two $N$-mode point contacts to electron reservoirs, is studied as a measure of the crossover from stochastic quantum transport to deterministic classical transport. The transition proceeds through the formation of {\em fully} transmitted or reflected scattering states, which we construct explicitly. The fully transmitted states contribute to the mean current $\bar{I}$, but not to the shot-noise power $S$. We find that these noiseless transmission channels do not exist for $N\alt\sqrt{k_{F}L}$, where we expect the random-matrix result $S/2e\bar{I}=1/4$. For $N\agt\sqrt{k_{F}L}$ we predict a suppression of the noise $\propto (k_{F}L/N^{2})^{N\delta/\pi\hbar\lambda}$. This nonlinear contact dependence of the noise could help to distinguish ballistic chaotic scattering from random impurity scattering in quantum transport.