Origin of the log-periodic oscillations in the quantum dynamics of electrons in quasiperiodic systems

Abstract

Recently, the occurrence of log-periodic oscillations in the quantum dynamics of electrons was reported for the one-dimensional Fibonacci quasicrystal by Lifshitz and Even-Dar Mandel. We apply a real-space renormalization group approach to show that these log-periodic oscillations are related to the underlying quasiperiodic structure of the Fibonacci quasicrystal. We find that they originate from the superposition of bonding and antibonding states associated to strongly coupled atoms in the chains, and that they show a hierarchical structure closely related to the atomic configurations.

Keywords:

• quantum diffusion
• Fibonacci quasicrystal
• mean square displacement
• return probability
• log-periodic oscillations

Acknowledgements

The author thanks Ron Lifshitz for helpful discussions. This research was supported by a Marie Curie Intra European Fellowship within the 7th European Community Framework Programme.

Notes

No potential conflict of interest was reported by the author.