Spectrum of an oscillator with jumping frequency and the interference of partial susceptibilities

TL;DR

This paper analyzes the spectrum of an underdamped oscillator with jumping frequencies caused by shot-noise fluctuations, revealing interference effects and spectral structures relevant to nano-mechanical systems.

Contribution

It provides an analytical description of the oscillator spectrum considering frequency jumps and interference, applicable to nano-mechanical resonators with fluctuating attached molecules.

Findings

Spectrum exhibits fine structure or a single asymmetric peak depending on parameters.

Analytical form derived for nano-mechanical resonators with fluctuating molecules.

Interference of susceptibilities explains spectral features in systems with correlated frequency jumps.

Abstract

We study an underdamped oscillator with shot-noise frequency fluctuations. The oscillator spectrum is determined by the interference of the susceptibilities for different eigenfrequencies. Depending on the parameters, it has a fine structure or displays a single asymmetric peak. For nano-mechanical resonators with a fluctuating number of attached molecules, the spectrum is found in a simple analytical form. The results bear on various types of systems where the reciprocal correlation time of frequency fluctuations can be comparable to the typical frequency jumps.