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

Abstract

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.

15,CPT-94/P.3003,tex,0

References in corpus (3)

• Trace maps, invariants, and some of their applications
• Non-periodic Ising quantum chains and conformal invariance
• Exciton Optical Absorption in Self-Similar Aperiodic Lattices

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• Spectra of Discrete Schrödinger Operators with Primitive Invertible Substitution Potentials
• Periodic features in the Dynamic Structure Factor of the Quasiperiodic Period-doubling Lattice
• Continuum Schrödinger Operators Associated With Aperiodic Subshifts
• Emergence of quasiperiodic Bloch wave functions in quasicrystals
• Tight Binding Hamiltonians and Quantum Turing Machines
• Quantum chaos in quantum Turing machines
• Spectrum and diffusion for a class of tight-binding models on hypercubes
• Self-adjoint extension approach for singular Hamiltonians in (2+1) dimensions
• Transmission and Spectral Aspects of Tight Binding Hamiltonians for the Counting Quantum Turing Machine
• Chaos-based Potentials in the One-dimensional Tight-binding Model Probed by the Inverse Participation Ratio
• Quantum network architecture of tight-binding models with substitution sequences