Time evolution in classical harmonic oscillator chains on periodic and aperiodic lattices.

摘要

To study the dynamics of classical harmonic oscillator (H.O.) chains on an aperiodic lattice by the Recurrence Relations method (RR method), we have first studied classical H.O. chains on a periodic lattice. Based on this analysis, we have constructed the Georgia (G)-ring as our model of H.O. chain on an aperiodic lattice (Fibonacci lattice) and also obtained the dimensionality d and the hypersurface ;For a H.O. chain on an aperiodic lattice, it would be unlikely to find an analytic expression for the dispersion relation. Hence we need to obtain it numerically. For this purpose we have employed the RR3 instead of the RR2. By this approach we have obtained the dispersion relation numerically and also investigated the distribution of zeros of the relaxation function in the G-ring.