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The phase diffusion in a self-sustained oscillator, which producesoscillator's spectral linewidth, is inherently governed by a nonlinear Langevinequation. Over past 40 years, the equation has been treated with linearapproximation, rendering the nonlinearity's effects unknown. Here we solve thenonlinear Langevin equation using the perturbation method borrowed from quantummechanics, and reveal the physics of the nonlinearity: slower phase diffusion(linewidth narrowing) and a surprising oscillation frequency shift thatformally corresponds to the Lamb shift in quantum electrodynamics.

Phase Diffusion and Lamb-Shift-Like Spectrum Shift in Classical Oscillators