Observation of Log-Periodic Oscillations in the Quantum Dynamics of Electrons on the One-Dimensional Fibonacci Quasicrystal
arXiv:1006.0688 · doi:10.1080/14786435.2010.543092
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.
References in corpus (12)
- Direct observation of a localization transition in quasi-periodic photonic lattices
- Quasicrystals: A matter of definition
- The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian
- Gordon-type arguments in the spectral theory of one-dimensional quasicrystals
- What is a crystal?
- Physical Consequences of Complex Dimensions of Fractals
- Electronic Energy Spectra of Square and Cubic Fibonacci Quasicrystals
- Connection between energy-spectrum self-similarity and specific heat log-periodicity
- Electronic energy spectra and wave functions on the square Fibonacci tiling
- Wave Packet Dynamics, Ergodicity, and Localization in Quasiperiodic Chains
- Electrons and Phonons on the Square Fibonacci Tiling
- Bloch-like Electronic Wave Functions in Two-Dimensional Quasicrystals