Abstract
The evolution equations for the density distribution and its two phase-space point correlation for nonlinear oscillators under the influence of an external random driving force are derived. We found that the correlation function obeys a Fokker-Planck-like evolution equation with decoherence, diffusion, and source terms. An asymptotic steady state solution is discussed, where the small-amplitude and short-wavelength spatial fluctuations of density ( microstructure'') are found to be the special effect of the coherent random driving, distinguishing it from incoherent noise.
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