Nonlinear damping and dephasing in nanomechanical systems

TL;DR

This paper develops a microscopic theory for nonlinear damping and dephasing in nano- and micro-mechanical systems, focusing on vibrational mode scattering and energy transfer mechanisms.

Contribution

It introduces a formalism that captures both uniform and nonuniform systems, accounting for thermal mode decay and identifying nonlinear analogs of classical damping mechanisms.

Findings

Dependence of relaxation parameters on temperature and geometry

Identification of nonlinear Landau-Rumer, thermoelastic, and Akhiezer mechanisms

Formalism applicable to spatially nonuniform systems

Abstract

We present a microscopic theory of nonlinear damping and dephasing of low-frequency eigenmodes in nano- and micro-mechanical systems. The mechanism of the both effects is scattering of thermally excited vibrational modes off the considered eigenmode. The scattering is accompanied by energy transfer of $2\hbar\omega_0$ for nonlinear damping and is quasieleastic for dephasing. We develop a formalism that allows studying both spatially uniform systems and systems with a strong nonuniformity, which is smooth on the typical wavelength of thermal modes but not their mean free path. The formalism accounts for the decay of thermal modes, which plays a major role in the nonlinear damping and dephasing. We identify the nonlinear analogs of the Landau-Rumer, thermoelastic, and Akhiezer mechanisms and find the dependence of the relaxation parameters on the temperature and the geometry of a system.