Finite frequency quantum noise in an interacting mesoscopic conductor

TL;DR

This paper provides a quantum scattering theory analysis of frequency-dependent current noise in an interacting mesoscopic cavity, revealing how Coulomb interactions and two characteristic time scales influence noise behavior at high frequencies.

Contribution

It introduces a detailed quantum calculation incorporating Coulomb interactions and identifies the impact of dwell and RC times on noise at high frequencies.

Findings

Noise exhibits features at frequencies near the inverse charge relaxation time.

Explicit dependence of noise on dwell time and RC time scales.

Interactions significantly modify the frequency dependence of quantum noise.

Abstract

We present a quantum calculation based on scattering theory of the frequency dependent noise of current in an interacting chaotic cavity. We include interactions of the electron system via long range Coulomb forces between the conductor and a gate with capacitance $C$. We obtain explicit results exhibiting the two time scales of the problem, the cavity's dwell time $\tau_D$ and the $RC$-time $\tau_C$ of the cavity {\em vis \`a vis} the gate. The noise shows peculiarities at frequencies of the order and exceeding the inverse charge relaxation time $\tau^{-1} = \tau^{-1}_D+\tau^{-1}_C $.