Periodic almost-Schrödinger equation for quasicrystals

  title={Periodic almost-Schr{\"o}dinger equation for quasicrystals},
  author={Igor V. Blinov},
  journal={Scientific Reports},
  • I. Blinov
  • Published 29 September 2014
  • Physics
  • Scientific Reports
A new method for finding electronic structure and wavefunctions of electrons in quasiperiodic potential is introduced. To obtain results it uses slightly modified Schrödinger equation in spaces of dimensionality higher than physical space. It enables to get exact results for quasicrystals without expensive non-exact calculations. 

A Hamiltonian model of the Fibonacci quasicrystal using non-local interactions: simulations and spectral analysis

Abstract This article presents a Hamiltonian architecture based on vertex types and empires for demonstrating the emergence of aperiodic order in one dimension by a suitable prescription for breaking

Localization-delocalization transition in spin-orbit-coupled Bose-Einstein condensate

This work explains why simultaneous Rabi and SO coupling are necessary ingredients for LDT threshold cancellation and shows that strong SO coupling drives the system into the state where its evolution becomes similar to the evolution of a one-component system.



Quasicrystals: a new class of ordered structures

A quasicrystal is the natural extension of the notion of a crystal to structures with quasiperiodic, rather than periodic, translational order. We classify two- and three-dimensional quasicrystals by

Computation and visualization of photonic quasicrystal spectra via Bloch's theorem

Previous methods for determining photonic quasicrystal (PQC) spectra have relied on the use of large supercells to compute the eigenfrequencies and/or local density of states. In this paper, we

Embedding quasicrystals in a periodic cell: dynamics in quasiperiodic structures.

This work introduces a construction to "periodize" a quasiperiodic lattice of obstacles, i.e., embed it into a unit cell in a higher-dimensional space, reversing the projection method used to form quasilattices, and finds superdiffusion in the presence of channels, and a subdiffusive regime when obstacles overlap.

Numerical methods for quasicrystals

Four-dimensional quantum Hall effect in a two-dimensional quasicrystal.

It is shown that a previously inaccessible phase of matter-the 4D integer quantum Hall effect-can be incorporated in a 2D quasicrystal, and may pave the way to the experimental study of 4D physics.

Higher-dimensional approach to a unified growth model for crystals, quasicrystals, and multiply twinned particles.

On formule le modele de la croissance decaedrique recursif (DR), qui genere aussi bien les cristaux que les quasicristaux de toutes symetries, dans le contexte de la methode de la projection coupee.

Electronic properties of quasicrystals an experimental review

  • S. Poon
  • Physics, Materials Science
  • 1992
Abstract The electronic properties of a large number of icosahedral-crystal systems have been studied experimentally. These systems include alloys of the simple metals and those that contain

Almost periodic Schrödinger operators: A Review

Metallic Phase with Long-Range Orientational Order and No Translational Symmetry

We have observed a metallic solid (Al-14-at.%-Mn) with long-range orientational order, but with icosahedral point group symmetry, which is inconsistent with lattice translations. Its diffraction

Et al

A large population-based survey of veterans and nondeployed controls found evidence of a deployment-related Gulf War syndrome by factor analysis in Air Force veterans and controls.