Semiclassical approach to the ac-conductance of chaotic cavities

TL;DR

This paper extends semiclassical quantum transport theory to analyze frequency-dependent conductance in chaotic mesoscopic cavities, confirming and generalizing random matrix results while exploring effects like Ehrenfest time, tunnel barriers, and dephasing.

Contribution

It develops a semiclassical framework for ac conductance in chaotic cavities, including Ehrenfest time effects and tunnel barriers, and studies dephasing impacts on charge relaxation resistance.

Findings

Confirmed random matrix results for ac conductance.

Generalized conductance calculations including Ehrenfest time effects.

Analyzed dephasing influence on mesoscopic capacitor resistance.

Abstract

We address frequency-dependent quantum transport through mesoscopic conductors in the semiclassical limit. By generalizing the trajectory-based semiclassical theory of dc quantum transport to the ac case, we derive the average screened conductance as well as ac weak-localization corrections for chaotic conductors. Thereby we confirm respective random matrix results and generalize them by accounting for Ehrenfest time effects. We consider the case of a cavity connected through many leads to a macroscopic circuit which contains ac-sources. In addition to the reservoir the cavity itself is capacitively coupled to a gate. By incorporating tunnel barriers between cavity and leads we obtain results for arbitrary tunnel rates. Finally, based on our findings we investigate the effect of dephasing on the charge relaxation resistance of a mesoscopic capacitor in the linear low-frequency regime.