Observation of log-periodic oscillations in the quantum dynamics of electrons on the one-dimensional Fibonacci quasicrystal

Abstract

We revisit the question of quantum dynamics of electrons on the off-diagonal Fibonacci tight-binding model. We find that typical dynamical quantities, such as the probability of an electron to remain in its original position as a function of time, display log-periodic oscillations on top of the leading-order power-law decay. These periodic oscillations with the logarithm of time are similar to the oscillations that are known to exist with the logarithm of temperature in the specific heat of Fibonacci electrons, yet they offer new possibilities for the experimental observation of this unique phenomenon.

Keywords:

• quasicrystals
• Fibonacci quasicrystals
• tight-binding model
• electronic transport
• quantum dynamics
• log-periodic oscillations

Acknowledgements

We wish to thank Amnon Aharony for fruitful discussions and for suggesting that the “wiggles” in our numerical data might be real. We also thank Eric Akkermans and Eli Eisenberg for helpful discussions. This research is supported by the Israel Science Foundation through Grant Nos. 684/06 and 556/10.