Phonon-mediated thermal conductance of mesoscopic wires with rough edges

We present an analysis of acoustic-phonon propagation through long, free-standing, insulating wires with rough surfaces. Owing to a crossover from ballistic propagation of the lowest-frequency phonon mode at omega < omega(1) = pi c/W to a diffusive (or even localized) behavior upon;the increase of phonon frequency, followed by reentrance into the quasiballistic regime, the heat conductance:of a wire acquires an intermediate tendency to saturate within the temperature range T similar to (h) over bar omega(1)/k(B). [S0163- 1829(99)02543-6].