Anomalous diffusion in nonlinear oscillators with multiplicative noise

The time-asymptotic behavior of undamped, nonlinear oscillators with a random frequency is investigated analytically and numerically. We find that averaged quantities of physical interest such as the oscillator's mechanical energy, root-mean-square position, and velocity grow algebraically with time. The scaling exponents and associated generalized diffusion constants are calculated when the oscillator's potential energy grows as a power of its position: U(x)similar tox(2n) for \x\-->infinity. Correlated noise yields anomalous diffusion exponents equal to half the value found for white noise.