Dresden 2020 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 13: Glasses and Glass Transition (joint session DY/CPP)

DY 13.3: Talk

Monday, March 16, 2020, 15:45–16:00, ZEU 118

Efficient algorithm to study dynamics in the transition between quasiperiodic and disordered environments — •Alan Rodrigo Mendoza Sosa and Atahualpa Kraemer — Universidad Nacional Autónoma de México, Mexico City, Mexico

Crystals have translational and rotational symmetries while quasicrystals have rotational symmetry in a single point, and glasses have none. This is revealed in the diffraction pattern, where crystals and quasicrystals have a discrete pattern, but quasicrystals exhibit forbidden symmetries, while glasses have a continuous pattern. Increment the rotational symmetry of quasicrystals should produce a denser diffraction pattern, closer to the continuous pattern exhibit in glasses. Motivated with the previous arguments we propose to study the structure of a quasiperiodic array and the dynamics of particles in quasiperiodic environments when the folding symmetry increases. However, the usual techniques to produce quasiperiodic arrays are aimed at producing arrays of low symmetries and near to the center of symmetry, then it becomes time expensive to perform simulations. In this work, we present an algorithm to produce quasiperiodic arrays with arbitrary symmetry around any point in the space, based on the generalized dual method. Also, using the Voronoi tessellation of the quasiperiodic array, and the incremental algorithm to track particles, we made an algorithm to perform simulations of particles moving in a quasiperiodic potential with arbitrary symmetry. We apply this algorithm to a quasiperiodic Lorentz gas with high symmetry to study diffusion and compare it with the random Lorentz Gas.