Tunneling and Quantum Noise in 1-D Luttinger Liquids

TL;DR

This paper investigates non-equilibrium noise in 1-D Luttinger liquids and fractional quantum Hall edges, revealing how tunneling event correlations produce characteristic high- and low-frequency noise behaviors.

Contribution

It introduces a Coulomb gas and diagrammatic approach to analyze tunneling statistics and noise spectra in non-equilibrium quantum liquids, highlighting the persistence of the ||| noise singularity.

Findings

High-frequency noise exhibits an algebraic singularity at  = e*V/.

Low-frequency noise is dominated by inter-dipole correlations, leading to a || spectrum.

Higher-order interactions mainly affect the amplitude, not the form, of the noise spectrum.

Abstract

We study non-equilibrium noise in the transmission current through barriers in 1-D Luttinger liquids and in the tunneling current between edges of fractional quantum Hall liquids. The distribution of tunneling events through narrow barriers can be described by a Coulomb gas lying in the time axis along a Keldysh (or non-equilibrium) contour. The charges tend to reorganize as a dipole gas, which we use to describe the tunneling statistics. Intra-dipole correlations contribute to the high-frequency ``Josephson'' noise, which has an algebraic singularity at $\omega=e^*V/\hbar$, whereas inter-dipole correlations are responsible for the low-frequency noise. Inter-dipole interactions give a $1/t^2$ correlation between the tunneling events that results in a $|\omega|$ singularity in the noise spectrum. We present a diagrammatic technique to calculate the correlations in perturbation theory, and show that contributions from terms of order higher than the dipole-dipole interaction should only affect the strength of the $|\omega|$ singularity, but its form should remain $\sim |\omega|$ to all orders in perturbation theory.