Quantum dynamics in high codimension tilings: from quasiperiodicity to disorder

Abstract

We analyze the spreading of wavepackets in two-dimensional quasiperiodic and random tilings as a function of their codimension, i.e. of their topological complexity. In the quasiperiodic case, we show that the diffusion exponent that characterizes the propagation decreases when the codimension increases and goes to 1/2 in the high codimension limit. By constrast, the exponent for the random tilings is independent of their codimension and also equals 1/2. This shows that, in high codimension, the quasiperiodicity is irrelevant and that the topological disorder leads in every case, to a diffusive regime, at least in the time scale investigated here.

4 pages, 5 EPS figures

References in corpus (4)

• How to escape Aharonov-Bohm cages ?
• Quantum dynamics in two and three-dimensional quasiperiodic tilings
• Diffusion of electrons in random magnetic fields,
• Flip dynamics in octagonal rhombus tiling sets

Cited by in corpus (7)

• Spectral and Diffusive Properties of Silver-Mean Quasicrystals in 1,2, and 3 Dimensions
• Renormalization Group Approach for the Wave Packet Dynamics in Golden-Mean and Silver-Mean Labyrinth Tilings
• Energy levels and their correlations in quasicrystals
• Electronic states of a disordered 2D quasiperiodic tiling: from critical states to Anderson localization
• Random tilings of high symmetry: I. Mean-field theory
• Quasiperiodic Heisenberg antiferromagnets in two dimensions
• Estimating the asymptotics of solid partitions