Energy spectra and eigenstates of quasiperiodic tight-binding Hamiltonians

Abstract

Analytic and numerical results for quasiperiodic tight-binding models are reviewed, with emphasis on two and three-dimensional models which so far are beyond a mathematically rigorous treatment. In particular, we consider energy spectra of aperiodic tight-binding models and the corresponding level statistics, which are well reproduced by random matrix theory. The eigenstates are characterised by multifractal analysis, and a construction of peculiar multifractal states on the Penrose tiling is discussed. We also consider quantum diffusion, and present some results on interacting electron systems in one dimension.

arXiv comment27 pages, 27 PostScript figures, LaTeX using vch-book.cls

References in corpus (20)

• What determines the spreading of a wave packet?
• Asymptotics of Universal Probability of Neighboring Level Spacings at the Anderson Transition
• Trace maps, invariants, and some of their applications
• Relation between Energy Level Statistics and Phase Transition and its Application to the Anderson Model
• Trace and antitrace maps for aperiodic sequences, their extensions and applications
• Gordon-type arguments in the spectral theory of one-dimensional quasicrystals
• Energy spectra, wavefunctions and quantum diffusion for quasiperiodic systems
• Interacting particles at a metal-insulator transition
• Level-Spacing Distributions of Planar Quasiperiodic Tight-Binding Models
• Exact Eigenstates of Tight-Binding Hamiltonians on the Penrose Tiling
• Localization properties of two interacting particles in a quasi-periodic potential with a metal-insulator transition
• Energy level statistics of electrons in a 2D quasicrystal
• What is Aperiodic Order?
• Universal level-spacing statistics in quasiperiodic tight-binding models
• Application of random matrix theory to quasiperiodic systems
• Electronic states in topologically disordered systems
• Energy Levels of Quasiperiodic Hamiltonians, Spectral Unfolding, and Random Matrix Theory
• Self-similarity under inflation and level statistics: a study in two dimensions
• Dynamical Scaling Properties of Electrons in Quantum Systems with Multifractal Eigenstates
• Magnetotransport in Quasilattices

Cited by in corpus (6)

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• Rydberg Noisy-Dressing and applications in making soliton-molecules and droplet quasi-crystals
• Level-spacing distributions of the Gaussian unitary random matrix ensemble
• The Fibonacci quasicrystal: case study of hidden dimensions and multifractality
• The Unexpected Fractal Signatures in Fibonacci chains