Shot-noise of quantum chaotic systems in the classical limit

TL;DR

This paper investigates shot-noise in quantum chaotic systems within the deep classical limit, revealing that transmission becomes noiseless with perfect coupling and providing universal shot-noise results for systems with tunnel barriers.

Contribution

It presents new semiclassical results for shot-noise in the classical limit, extending understanding beyond random matrix theory applicability.

Findings

Transmission eigenvalues are 0 or 1 with perfect coupling, leading to noiseless transmission.

Universal shot-noise results are derived for systems with tunnel barriers.

Random matrix theory no longer applies in the deep classical limit.

Abstract

Semiclassical methods can now explain many mesoscopic effects (shot-noise, conductance fluctuations, etc) in clean chaotic systems, such as chaotic quantum dots. In the deep classical limit (wavelength much less than system size) the Ehrenfest time (the time for a wavepacket to spread to a classical size) plays a crucial role, and random matrix theory (RMT) ceases to apply to the transport properties of open chaotic systems. Here we summarize some of our recent results for shot-noise (intrinsically quantum noise in the current through the system) in this deep classical limit. For systems with perfect coupling to the leads, we use a phase-space basis on the leads to show that the transmission eigenvalues are all 0 or 1 -- so transmission is noiseless [Whitney-Jacquod, Phys. Rev. Lett. 94, 116801 (2005), Jacquod-Whitney, Phys. Rev. B 73, 195115 (2006)]. For systems with tunnel-barriers on the leads we use trajectory-based semiclassics to extract universal (but non-RMT) shot-noise results for the classical regime [Whitney, Phys. Rev. B 75, 235404 (2007)].