1/f noise: A nonlinear-generalized-Langevin-equation approach

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The spectrum of the autocorrelation function of the velocity fluctuations is calculated by using the nonlinear generalized Langevin equation which has a random force which is a function of the coordinates of the Brownian particle. We show that while the Nyquist noise and the persistent correlation can be obtained by using the linear generalized Langevin equation, the extra contribution to the noise spectrum due to the nonlinear effect in the nonlinear generalized Langevin equation is inversely proportional to the total number of particles and to a negative power of the frequency. In a hydrodynamic calculation, we derive a formula for the excess noise which has a frequency dependence -(4-d)/2 for the two- and three-dimensional cases (d=2 and 3, respectively). A detailed analysis shows that our two-dimensional excess-noise formula agrees with the empirical Hooge formula, and the theoretical form of the Hooge parameter which we obtain is consistent with the known experimental results. In a many-body calculation, similar results are obtained. Physically, we argue that the 1/f noise arises from at least two basic phenomena: (a) vorticity diffusion in the classical case (or weak localization in the quantum case), and (b) the deviation of the diffusion coefficient from its conventional value due to boundary confinement effects or effects due to low dimensionality. © 1990 The American Physical Society.

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Physical Review B

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