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

摘要

We revisit the question of quantum dynamics of electrons on the off-diagonalFibonacci tight-binding model. We find that typical dynamical quantities, suchas the probability of an electron to remain in its original position as afunction of time, display log-periodic oscillations on top of the leading-orderpower-law decay. These periodic oscillations with the logarithm of time aresimilar to the oscillations that are known to exist with the logarithm oftemperature in the specific heat of Fibonacci electrons, yet they offer newpossibilities for the experimental observation of this unique phenomenon.