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We study phonon-mediated damping of mechanical vibrations in a finitequantum-mechanical atomic-chain model. Our study is motivated by the quest tounderstand the quality factors (Q) of nanomechanical resonators andnanoelectromechanical systems (NEMS), as well as actual experiments withsuspended atomic chains and molecular junctions. We consider a finite atomicchain which is coupled to a zero-temperature outer environment, modeled as twoadditional semi-infinite chains, thus inducing "clamping-losses". Weak couplingto the outer environment ensures that the clamping losses are small, and thatthe initially discrete nature of the phonon spectrum is approximatelymaintained. We then consider a phonon damping process known as "Landau-Rumerdamping", where phonons in the excited mode of vibration decay into other modesthrough anharmonic phonon-phonon interaction. The approximately discrete natureof the phonon spectrum leads to sharp nonmonotonic changes in Q as parametersare varied, and to the appearance of resonances in the damping. The lattercorrespond to the existence of decay processes where the participating phononsapproximately conserve energy. We explore means to control the damping bychanging either the number of atoms in the chains or the ratio between thelongitudinal and transverse speeds of sound, thereby suggesting futureexperiments to observe this resonance-like behavior.

Phonon-mediated damping of mechanical vibrations in a finite atomic chain coupled to an outer environment