Pink noise in Electric Current from Amplitude Modulations

TL;DR

This paper investigates the origin of pink noise in electric currents, proposing that amplitude modulation of waves causes 1/f fluctuations, and verifies this through a model involving electron wave packets and demodulation processes.

Contribution

It introduces a novel explanation for pink noise based on amplitude modulation and demonstrates this mechanism in electric current systems and nerve firing models.

Findings

Electric current fluctuations exhibit 1/f noise after wave squaring.

Demodulation reveals underlying amplitude modulation causing pink noise.

Nerve firing sequences also show 1/f fluctuations after thresholding.

Abstract

We recently proposed that the general origin of 1/f fluctuation, or pink noise, is the amplitude modulation (or beat) of many waves with accumulating frequencies. In this paper, we verify this proposal in the electric current system. We use the classical Langevin equation to describe the electron wave packets flowing in the (semi-)conductor, affected by the back reaction of soft photon emission. If this were amplitude modulation, a demodulation process is needed to extract the fluctuation features. We first square the wave packet, which corresponds to the electric current, and obtain the 1/f fluctuation in this current data. We further speculate that this wave packet, after demodulation by thresholding, triggers the time sequence of the nerve firing. In our model, this also shows 1/f fluctuations, which is quite robust.