1212.3326 (Kai Jiang et al.)

Numerical Methods for Quasicrystals    [PDF]

Kai Jiang, Pingwen Zhang

A new projection method, implemented in higher-dimensional reciprocal space, is developed to compute quasicrystals. The approach enables us to represent quasicrystals as periodic structures in higher-dimensional space. A proposed projective matrix can project a higher-dimensional periodic structure into a quasicrystal in physical space. Compared with the traditional crystalline approximant method, the projection method overcomes the restrictions of the Simultaneous Diophantine Approximation, and can use periodic boundary conditions conveniently. Meanwhile, the proposed method can efficiently reduce the computational complexity through implementing in a unit cell and using pseudospectral method. By applying the projection method to the Lifshitz-Petrich model, we can compute quasicrystals rather than crystalline approximants, maintaining the rotational symmetry accurately. More significantly, the algorithm can calculate the free energy density to high precision.

View original: http://arxiv.org/abs/1212.3326