Phonon transport and thermal conductivity in an acoustic filter

We investigate the phonon ballistic transmission and the thermal conductivity in a dielectric quantum structure. It is found that these observable quantities sensitively depend on geometric parameters, and are of quantum character. The total transmission coefficient as a function of the reduced waveguide-length exhibits periodical behaviour and the reduced thermal conductance decreases below the ideal universal value for the low temperature. Our results show that one can control the thermal conductivity of the structure and make all kinds of acoustic filters to match practical requirements in devices by adjusting the geometric parameters.