ANOMALOUS SCALING BEHAVIOR OF FOURIER SPECTRA IN A ONE-DIMENSIONAL HIERARCHICAL LATTICE

Fourier spectral properties of a one-dimensional hierarchical lattice are studied by using the recursion relation of the Fourier amplitudes G(N)(q). It is found that the scaling exponents of dominant peaks depe nd on the potential parameter R. For R>2, G(N)(q) exhibits anomalous s caling behavior with a scaling exponent log2 R for any rational value of the wave number q. On the other hand, for R<2, the scaling exponent s of dominant peaks are unity; i.e., the growth of G(N)(q) is of the o rder of the system size N. At R = 2, the growth behavior is characteri zed by a logarithmic correction. The transition phenomenon in the Four ier spectrum resembles a dynamical phase transition occurring in the c lassical diffusion problem.