Quantum dynamics in high codimension tilings: from quasiperiodicity to disorder

TL;DR

This paper investigates how wavepacket spreading in two-dimensional quasiperiodic and random tilings depends on their topological complexity, revealing that high codimension quasiperiodic systems behave similarly to disordered ones, both exhibiting diffusion with an exponent of 1/2.

Contribution

It demonstrates that in high codimension, quasiperiodic systems lose their unique spreading properties and behave like disordered systems, leading to universal diffusive behavior.

Findings

Diffusion exponent decreases with codimension in quasiperiodic tilings.

High codimension quasiperiodic tilings exhibit a diffusion exponent of 1/2.

Random tilings show a diffusion exponent of 1/2 regardless of codimension.

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.