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

摘要

The 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 ν_1 and ν_2; 2) the application of the e - e FP to materials and its-steady state solution that depends on ν_1(υ), ν_2(υ), and the square a~2 of the acceleration a = eE/m; 3) the steady-state solution of the e - e FP equation becomes similar to the Fermi-Dirac distribution function if a~2 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 a_(ZPF)~2 that for any conduction current there is always a small interval δυ for the electron speed υ where ν_1 ∝ ν_2 ∝ 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/f~(1-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.