The subject of electronic and phonon states in crystals with incommensurate periodic
potentials is reviewed. The emphasis is on the physics behind the various theoretical …

The aim of this work is to present a comprehensive and up-to-date review of the main
physical properties (such as energy profiles, localization, scale laws, multifractal analysis …

Recent theories of scaling in quasiperiodic dynamical systems are applied to the behavior of
a particle in an almost periodic potential. A special tight-binding model is solved exactly by a …

We show that a one-dimensional tight-binding electron moving in a slowly varying potential,
V n= λ cos (α n ν), where n is the site index and 0< ν< 1, has a mobility edge in its spectrum …

The development of the concept of quasicrystals has challenged many widely held
assumptions of crystallography and solid state physics. It had been generally assumed that …

The subject I would like to present here today pretends to use C"-algebras in concrete
problems of modern physics, a mathematical tool which have been liable to controversies …

Physics Spectral Properties of One Dimensional Quasi-Crystals Page 1 Communications in
Commun. Math. Phys. 125, 527-543 (1989) MathβlTiatlCal Physics © Springer-Verlag 1989 …

We study the localization properties of the one-dimensional nearest-neighbor tight-binding
Schrödinger equation, u n+ 1+ un− 1+ V nun= Eu n, where the on-site potential V n is neither …

Results of a renormalization-group analysis augmented by numerical calculations are
presented for the electronic and phonon properties of a one-dimensional quasiperiodic …

Quantum Mechanics was born in 1900, when Planck [PL00] investigated the laws of black
body radiation. He found the correct formula for the power spectrum in terms of the light …