1/f noise and quantum indeterminacy

TL;DR

This paper develops a quantum-based approach to understanding 1/f voltage noise in conductors, revealing a fundamental lower bound on noise power spectrum related to quantum indeterminacy, and compares it with experimental data.

Contribution

It introduces a quantum uncertainty framework for 1/f noise, deriving a lower bound on the power spectrum and applying the Schwinger-Keldysh method for explicit calculation.

Findings

A lower bound on the 1/f noise power spectrum is established.

The calculated bound matches experimental measurements within a few times.

Quantum indeterminacy influences voltage fluctuation spectra at low frequencies.

Abstract

An approach to the problem of 1/f voltage noise in conductors is developed based on an uncertainty relation for the Fourier-transformed signal. The quantum indeterminacy caused by non-commutativity of the observables at different times makes the voltage autocovariance ambiguous, but the power spectrum of fluctuations remains well-defined. It is shown that a lower bound on the power spectrum exists, which is related to the antisymmetric part of the voltage correlation function. Using the Schwinger-Keldysh method, this bound is calculated explicitly in the case of unpolarized charge carriers with a parabolic dispersion, and is found to have a 1/f low-frequency asymptotic. A comparison with the 1/f-noise measurements in InGaAs quantum wells is made which shows that the observed noise levels are only a few times higher than the bound established.