  Generic properties of elastic phonon transport at a disordered interface are
studied. The results show that phonon transmittance is a strong function of
frequency and the disorder correlation length. At frequencies lower than the
van Hove singularity the transmittance at a given frequency increases as the
correlation length decreases. At low frequencies, this is reflected by
different power-laws for phonon conductance across correlated and uncorrelated
disordered interfaces which are in approximate agreement with perturbation
theory of an elastic continuum. These results can be understood in terms of
simple mosaic and two-colour models of the interface.
