Gy. Oh et al., ANOMALOUS SCALING BEHAVIOR OF FOURIER SPECTRA IN A ONE-DIMENSIONAL HIERARCHICAL LATTICE, Journal of the Korean Physical Society, 26(3), 1993, pp. 298-301
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.