Shot noise in chaotic systems: "classical" to quantum crossover

TL;DR

This paper investigates how shot noise in chaotic systems transitions from classical to quantum behavior, depending on the ratio of dwell time to diffraction time, providing a potential method to measure the Lyapunov exponent.

Contribution

It introduces a theoretical framework linking shot noise crossover to the Lyapunov exponent in chaotic systems, highlighting a new way to measure quantum chaos.

Findings

Shot noise vanishes when diffraction time exceeds dwell time.

Shot noise reaches a universal quantum value when diffraction time is much shorter.

Lyapunov exponent can be inferred from shot noise measurements.

Abstract

This paper is devoted to study of the classical-to-quantum crossover of the shot noise value in chaotic systems. This crossover is determined by the ratio of the particle dwell time in the system, $\tau_d$, to the characteristic time for diffraction $t_E \simeq \lambda^{-1} |\ln \hbar|$, where $\lambda$ is the Lyapunov exponent. The shot noise vanishes in the limit $t_E \gg \tau_d $, while reaches its universal quantum value in the opposite limit. Thus, the Lyapunov exponent of chaotic mesoscopic systems may be found by the shot noise measurements.