Noisy oscillator: Random mass and random damping.

The problem of a linear damped noisy oscillator is treated in the presence of two multiplicative sources of noise which imply a random mass and random damping. The additive noise and the noise in the damping are responsible for an influx of energy to the oscillator and its dissipation to the surrounding environment. A random mass implies that the surrounding molecules not only collide with the oscillator but may also adhere to it, thereby changing its mass.

Mass dependence of instabilities of an oscillator with multiplicative and additive noise.

We study the instabilities of a harmonic oscillator subject to additive and dichotomous multiplicative noise, focusing on the dependence of the instability threshold on the mass. For multiplicative noise in the damping, the energy instability threshold is crossed as the mass is decreased, as long as the smaller damping is in fact negative. For multiplicative noise in the stiffness, the situation is more complicated and in fact the energy transition is reentrant for intermediate noise strength and damping.