FOURIER SPECTRAL PROPERTIES OF THE GENERALIZED FIBONACCI LATTICES

We study the Fourier spectral properties of the generalized Fibonacci lattices generated by a concurrent substitution rule (A --> A(n)B(m), B --> A). Using the recursion relations of a one-dimensional wavevecto r q which determine the scaling behavior of the Fourier spectral peaks , we show that a lattice belonging to the silver mean series (n > 1, m = 1) contains Bragg peaks while a lattice belonging to the copper mea n (CM) series (n = 1, m > 1) does not. In the CM lattice (n = 1, m = 2 ), we obtain the scaling exponent gamma(q) of the Fourier amplitude an d show that the order of the periodicity is in between those of the qu asiperiodic and the Thue-Morse lattices. Performing a multifractal ana lysis on the Fourier spectra of the CM and nickel mean (n = 1, m = 3) lattices, we show that these lattices have a singular continuous Fouri er spectral measure.