  We analyse the thermal properties of a harmonic chain with weak correlated
disorder. With the use of a perturbative approach we derive analytical
expressions for the time-evolution of the chain temperature and of the heat
flow when both ends of the chain are coupled to heat baths. Our analytical and
numerical results demonstrate that specific long-range correlations of the
isotopic disorder can suppress or enhance the vibrational modes in pre-defined
frequency windows. In this way one can arrange a frequency-selective heat flow
through disordered chains.
