Equilibrium of random classical electromagnetic radiation in the presence of a nonrelativistic nonlinear electric dipole oscillator

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Abstract
The scattering of random classical electromagnetic radiation by a nonrelativistic nonlinear electric dipole oscillator is calculated purely within classical physics using a perturbation expansion carried through second order in the nonlinear coupling constant. It is shown that the Rayleigh-Jeans radiation spectrum is an equilibrium distribution in the presence of such a nonlinear oscillator, while random radiation spectra given by Planck's law or by zero-point raditation are not equilibrium distributions but rather are altered by the scattering oscillator.