STEADY-STATE DISTRIBUTIONS FOR HARMONIC OSCILLATOR WITH VERY FAST FREQUENCY FLUCTUATIONS

摘要

The moment and probability steady-state characteristics of harmonic oscillator with frequency fluctuations in the form of white noise are investigated. Based on well-known functional approach, we derive integro-differential Kolmogorov equation for the joint probability density function of oscillator coordinate and velocity. For white Gaussian noise, using a set of equations for joint moments, we reconstruct the approximate form of coordinate and velocity distributions in the limit of small friction. As shown, these probability density functions do not exist for zero friction because they cannot be normalized.