Diffusion-induced dissipation and mode coupling in nanomechanical resonators

TL;DR

This paper investigates how a diffusing particle on a nanomechanical resonator causes energy dissipation and mode coupling, affecting the resonator's vibrational behavior and potential sensing applications.

Contribution

It introduces a detailed analysis of diffusion-induced dissipation and mode coupling in nanomechanical resonators, combining numerical and analytical methods.

Findings

Diffusing adsorbate causes energy dissipation through short-time correlations.

Dissipation is linear at large amplitudes and nonlinear at small amplitudes.

Particle diffusion mediates mode coupling, enabling energy transfer to excited modes.

Abstract

We study a system consisting of a particle adsorbed on a carbon nanotube resonator. The particle is allowed to diffuse along the resonator, in order to enable study of e.g. room temperature mass sensing devices. The system is initialized in a state where only the fundamental vibration mode is excited, and the ring-down of the system is studied by numerically and analytically solving the stochastic equations of motion. We find two mechanisms of dissipation, induced by the diffusing adsorbate. First, short-time correlations between particle and resonator motions means that the net effect of the former on the latter does not average out, but instead causes dissipation of vibrational energy. For vibrational amplitudes that are much larger than the thermal energy this dissipation is linear; for small amplitudes the decay takes the same form as that of a nonlinearly damped oscillator. Second, the particle diffusion mediates a coupling between vibration modes, enabling energy transfer from the fundamental mode to excited modes, which rapidly reach thermal equilibrium.