Tunneling and Quantum Noise in 1-D Luttinger Liquids

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 $\omega =e^{\ast }V/\hslash$, 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.

RevTex, 9 figures available upon request, cond-mat/yymmnnn

References in corpus (2)

• Noise in an ac biased junction. Non-stationary Aharonov-Bohm effect
• Contact Terms and Duality Symmetry in The Critical Dissipative Hofstadter Model

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