Behavior of the phonon gas in restricted geometries at low temperatures

In a previous paper [D.V. Anghel, J. P. Pekola, M. M. Leivo, J. K. Suoknuuti, and M.Manninen, Phys. Rev. Lett. 81, 2958 (1998)], we presented a formalism suitable to describe the thermal properties of the phonon gas in ultrathin membranes. We extend here the formalism to the case of narrow objects, such as wires or "bridges," and to the case of small nanoscopical objects. This will allow us to see crossovers between three-, two-, one- and zero-dimensional distribution of the phonon gas. [S0163-1829(99)10915-9].