Dynamics of axial channeling in quasicrystals:: An averaging-theory approach

A mathematically rigorous Hamiltonian theory of nonrelativistic axial channeling of positively charged particles in simply decorated icosahedral quasicrystals (IQCs) is developed in this paper on the basis of first-order averaging theory. The main result is an error estimate for the approximation of replacing the relevant Hamiltonian by that of the corresponding axial-continuum model to calculate suitable phase-space orbits. The derivation of this result makes essential use of a rigorous version of a theorem of Besjes on single-phase first-order averaging theory and of an asymptotic formula for the distribution of quasilattice points along arbitrary quasilattice axes of the considered IQC model. A deep number-theoretic result of Niederreiter is used to obtain this formula. (C) 2000 American Institute of Physics. [S0022-2488(00)03805-6].