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Zeitschrift Fur Physik B-Condensed Matter
We present an exact renormalization-group approach to study the local phonon properties of the double-atom generalized Fibonacci systems in which the masses and spring constants are all associated with the aperiodic sequences constructed by the inflation rule: {A, B} --> {A(n) B(m), A}. n(m + 1) basic transformations and 2n(n+m-1)+1 basic decimations are introduced. By applying the combinations of derived transformations and decimations, we can determine exactly the renormalized local environment, up to infinite order, of any given site in the double-atom systems. Both the single-atom and double-atom phonon models are employed, and the local density of states in several sites of some generalized Fibonacci systems are numerically calculated.
关键词: one-dimensional quasicrystals;quasi-periodic systems;thue-morse;lattices;electronic-properties;green-functions;cantor spectra;energy-spectra;chains;maps;localization
