The jump kinetics on a quasi-periodic pinning potential were analyzed under small external force conditions in a one-dimensional Fibonacci quasi-lattice model. The latter described the planar (layer) growth of stable quasi-crystals from the melt, and was also relevant to the movement of quasi-crystal dislocations under small stresses. An exact solution was found for the spectrum of jump lengths as function of the driving force. The solution described the supercooling dependence of the spectrum of nucleus heights upon the growing surface of a quasi-crystal. The spectrum appeared to be universal, and its shape exhibited a periodic dependence upon the logarithm of the supercooling. The resultant quasi-crystal growth kinetics agreed well with those found using computer simulations or the analysis of continuous thermodynamic models.

Jump Kinetics on the Fibonacci Quasi-Lattice - Exactly Solvable Model of Layer Growth and Dislocation Kinetics in Quasi-Crystals. M.A.Fradkin: Pisma Zhurnal Eksp. Teor. Fiz., 1999, 69[8], 531-6 (JETP Letters, 1999, 69[8], 570-6)