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 brieey review and explain the current status of mathematical results in this eld and discuss some conjectures and open problems.

The electronic spectra of quasi-regular systems grown following the Fibonacci sequence are investigated via simple one-dimensional tight-binding, one-band models. Different models are considered and the influence of the model parameters and the number of atoms entering the different blocks on the electronic spectrum are discussed. q 2005 Elsevier Ltd. All rights reserved.

We consider the evolution of a tight binding wave packet propagating in a time dependent potential. If the potential evolves according to a stationary Markov process, we show that the square amplitude of the wave packet converges, after diffusive rescaling, to a solution of a heat equation.

F. A. B. F. de Moura,1 A. V. Malyshev,2,* M. L. Lyra,1 V. A. Malyshev,3,† and F. Domínguez-Adame2,‡ 1Departamento de Física, Universidade Federal de Alagoas, 57072-970 Maceió, Alagoas, Brazil 2Departamento de Física de Materiales, Universidad Complutense, E-28040 Madrid, Spain 3Institute for Theoretical Physics and Materials Science Center, University of Groningen, Nijenborgh 4, 9747 AG Groning...

We study the ac-conductivity in linear response theory for the Anderson tight-binding model. We define the electrical acconductivity and calculate the linear-response current at zero temperature for arbitrary Fermi energy. In particular, the Fermi energy may lie in a spectral region where extended states are believed to exist.

We give explicit construction of vertex-transitive tight triangulations of d-manifolds for d ≥ 2. More explicitly, for each d ≥ 2, we construct two (d + 5d + 5)-vertex neighborly triangulated d-manifolds whose vertex-links are stacked spheres. The only other non-trivial series of such tight triangulated manifolds currently known is the series of non-simply connected triangulated d-manifolds wit...

It is not immediate whether a self-adjoint operator H with purely point spectrum implies absence of transport under the time evolution U(t) = e−iHt; in fact, it is currently known examples of Schrödinger operators with such kind of spectrum and transport. In case of tight-binding models on l2(IN) the transport is usually probed by the moments of order m > 0 of the position operator Xek = kek, t...

Janusz Jȩdrzejewski, Taras Krokhmalskii3,1,∗ and Oleg Derzhko3,4,† Institute of Theoretical Physics, University of Wroc law Max Born Sq. 9, 50-204 Wroc law, Poland Department of Theoretical Physics, University of Lódź 149/153 Pomorska Str., 90-236 Lódź, Poland Institute for Condensed Matter Physics 1 Svientsitskii Str., L’viv-11, 79011, Ukraine Chair of Theoretical Physics, Ivan Franko National...