STATISTICAL AND TRANSPORT-PROPERTIES OF QUASI-PERIODIC LAYERED STRUCTURES - THUE-MORSE AND FIBONACCI

Calculations are presented for the local density of phonon states scrD(2), the lattice specific heat Cv, and the transmission coefficient of a particle through a layered quasicrystal whose ends are fixed. In this paper, scrD(2) is obtained using a systematic decimation of the equations of motion for the atoms on a chain (where the two-dimensional plane is simulated by an atom) with the use of real-space renormalization-group techniques. The renormalized spring coupling constants for the atomic arrangement with the silver and golden means become invariant after the first decimation. However, the copper mean arrangement only becomes invariant after two decimations. We analyze the effect of this behavior in calculating the limiting case of a periodic chain from the Fibonacci series. We compare the generalized Fibonacci lattice with a lattice whose coupling constants are arranged in the Thue-Morse sequence. For the Fibonacci lattices, there is a significant difference between the copper mean results for the low-frequency density of states and those for the gold and silver lattices. This difference leads to a significant change in the specific heat for the copper relative to the periodic lattice. The density of states for the Thue-Morse chain has a unique low-frequency behavior and this also leads to a significant change in its specific heat at low temperature compared with a periodic lattice of the same length. © 1995 The American Physical Society.