arXiv subjects

J. -M. Ghez

Publications and source records attributed to J. -M. Ghez.

2 recordsLinked to original sources

arXiv1995

Schrödinger operators generated by substitutions

Schrödinger operators with potentials generated by primitive substitutions are simple models for one dimensional quasi-crystals. We review recent results on their spectral properties. These include in particular an algorithmically verifiable sufficient condition for their spectrum to be singular continuous and supported on a Cantor set of zero Lebesgue measure. Applications to specific examples are discussed.

cond-mat↗

arXiv1994

Remarks on the Spectral Properties of Tight Binding and Kronig-Penney Models with Substitution Sequences

We comment on some recent investigations on the electronic properties of models associated to the Thue-Morse chain and point out that their conclusions are in contradiction with rigorously proven theorems and indicate some of the sources of these misinterpretations. We briefly review and explain the current status of mathematical results in this field and discuss some conjectures and open problems.

cond-mat↗