Observation of Log-Periodic Oscillations in the Quantum Dynamics of Electrons on the One-Dimensional Fibonacci Quasicrystal

TL;DR

This paper reports the discovery of log-periodic oscillations in the quantum dynamics of electrons in a Fibonacci quasicrystal, revealing a novel oscillatory behavior in their probability decay over time.

Contribution

It demonstrates the presence of log-periodic oscillations in electron dynamics on the Fibonacci lattice, linking quantum behavior to previously observed thermodynamic oscillations.

Findings

Log-periodic oscillations observed in electron probability decay

Oscillations occur on top of power-law decay in dynamics

Potential for experimental detection of these oscillations

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.