Origin of 1/f noise as a runaway phenomenon due to the zeropoint field (ZPF) of quantum electrodynamics (QED)

Abstract

AbstractThe origin of electron transport noise whose power spectral density is inversely proportional to the frequency f has been realized after 80 years of attempts. Here we give its conceptual explanation that has required a sequence of five ideas and corresponding results: 1) The reduction of the nonlinear Boltzmann equation with electron‐electron (e –e) interaction to a Fokker‐Planck (denoted as e –e FP) equation containing two electron collision frequencies ν1 and ν2; 2) the application of the e –e FP to materials and its‐steady state solution that depends on ν1(υ), ν2(υ), and the square a2 of the acceleration a = e E/m; 3) the steadystate solution of the e –e FP equation becomes similar to the Fermi‐Dirac distribution function if a2 is considered as mainly due to the zero‐point field (ZPF) of quantum electrodynamics (QED) or, realistically, of stochastic electrodynamics (SED); 4) in this δυ range the e –e FP is similar to the usual FP solved by Stenflo when ν (υ) ∝ 1/υ. It is just because of aZPF that for any conduction current there is always a small interval δυ for the electron speed υ where ν1 ∝ ν2 ∝ 1/υ, condition that is at the threshold of runaways. The relevant time‐dependent Green solution of the e –e FP equation decreases as τ–ε with ε < 0.006. The consequent power spectral density S (f) turns out to be ∝ 1/f1–ε in an indefinite medium. Our S (f) also depends on the electrons concentration N and excellently fits the experimental data; 5) In a finite sample the memory or a fluctuation is preserved beyond the electron transit time because the transmission of information is mainly due to e –e interactions and to the diffusion coefficient that diverges at the threshold of runaways. A pimple (due to fluctuation) in the distribution function on the electron speeds is almost crystallized, decaying as τ–0.005 without any cut‐off at the transit time. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)