  We present analytical model and molecular dynamics simulations of phonon heat
transport in nanowires and nanoribbons with anharmonic lattices and dynamically
rough surfaces and edges. In agreement with recent experiments on heat
transport in single-crystalline silicon nanowires with rough surfaces, our
model and simulations predict finite and length-independent phonon thermal
conductivity in such quasi-one-dimensional systems, in contrast to anomalous
phonon thermal conductivity of corresponding momentum-conserving systems with
atomically smooth surfaces, divergent with the system length. Within our model,
the main cause of thermal conductivity reduction is momentum-nonconserving
scattering of longitudinal acoustic phonons by anharmonic side phonon leads in
quasi-one-dimensional phonon waveguide with dynamically rough surface or edge
layers.
