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Updated: Jun 18, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Analytical calculation of the frequency shift in phase oscillators driven by colored noise: implications for
1Department of Neurosciences, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106, USA. rfgalan@case.edu
Abstract:
We provide an analytical expression for the mean frequency shift in phase oscillators as a function of the standard deviation, sigma and the autocorrelation time, tau of small random perturbations. We show that the frequency shift is negative and proportional to sigma;{2} . Its absolute value increases monotonically with tau , approaching an asymptote determined by the L2 -norm of the phase-response curve. We validate our theoretical predictions with computer simulations and discuss their implications for the design of electronic oscillators and for the encoding of information in biological neural networks.
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