We consider a quantum model of a nanomechanical flexing beam resonator interacting with a bath comprising a few damped tunneling two level systems (TLS's). In contrast with a resonator interacting bilinearly with an ohmic free oscillator bath (modeling clamping loss, for example), the mechanical resonator damping is amplitude dependent, while the decoherence of quantum superpositions of mechanical position states depends only weakly on their spatial separation.
@article{arxiv.0907.0431,
title = {Damping and decoherence of a nanomechanical resonator due to a few two level systems},
author = {L. G. Remus and M. P. Blencowe and Y. Tanaka},
journal= {arXiv preprint arXiv:0907.0431},
year = {2009}
}