Phonon momentum and damping of mechanical resonators

TL;DR

This paper explores how phonon momentum influences the damping and amplification of vibrations in crystals, revealing a coupling between heat flow and mechanical oscillations that can be experimentally tested.

Contribution

It introduces a novel theoretical framework linking phonon momentum to macroscopic damping effects in resonators, supported by derivations of the governing equations.

Findings

Heat flow can sustain or damp vibrations in crystals.

Phonon momentum couples thermal and mechanical fields.

Experimental verification is feasible with current technology.

Abstract

The concept of physical momentum associated to phonons in a crystal, complemented with some fundamental reasoning, implies measurable effects in crystals even at a macroscopic scale. We show that, in close analogy with the transfer of momentum in the kinetic theory of gases, physical momentum carried by of phonons couples the thermal and the velocity field in a vibrating crystal. Therefore an heat flow applied to a vibrating crystal can sustain or damp the oscillation, depending on the interplay between the temperature and the velocity gradient. We derive the general equations of this effect and show that its experimental confirmation is within reach of current technology.