  The thermal conductance by phonons of a quasi-one-dimensional solid with
isotope or defect scattering is studied using the Landauer formalism for
thermal transport. The conductance shows a crossover from localized to Ohmic
behavior, just as for electrons, but the nature of this crossover is modified
by delocalization of phonons at low frequency. A scalable numerical
transfer-matrix technique is developed and applied to model
quasi-one-dimensional systems in order to confirm simple analytic predictions.
We argue that existing thermal conductivity data on semiconductor nanowires,
showing an unexpected linear dependence, can be understood through a model that
combines incoherent surface scattering for short-wavelength phonons with nearly
ballistic long-wavelength phonons. It is also found that even when strong
phonon localization effects would be observed if defects are distributed
throughout the wire, localization effects are much weaker when defects are
localized at the boundary, as in current experiments.
