Spectrum of an Oscillator with Jumping Frequency and the Interference of Partial Susceptibilities

We study an underdamped oscillator with random frequency jumps. We describe the oscillator spectrum in terms of coupled susceptibilities for different-frequency states. Depending on the parameters, the spectrum has a fine structure or displays a single asymmetric peak. For nanomechanical resonators with a fluctuating number of attached molecules, it is found in a simple analytical form. The results bear on dephasing in various types of systems with jumping frequency.