Lattice wave transmission through one-dimensional defected chain

By using Green's functional method, we investigated the influence of different strength constants at defected bonds and the junction's size on the transmission properties of the lattice wave in a one-dimensional chain. The heat currents of several defected chains are also calculated. The results show that correlation transmission between two defected bonds in a chain different from electron behaviors. Furthermore, for a large-size junction embedded in a chain, the transmission of high frequency phonons will disappear while having smaller strength constant in the junction than in two semi-infinity chains. On the other hand, for larger strength constant than in two semi-infinite chains, all phonons can transport through the junction with a certain transmission value, although the number of transmission peaks decreases. Finally, the lower frequency lattice waves have better transmission through a junction with a series of strength constants according to the Fibonacci sequence.