Cantor spectrum of graphene in magnetic fields

DOI10.1007/s00222-019-00916-yzbMath1447.82041arXiv1803.00988OpenAlexW3101588840WikidataQ127339815 ScholiaQ127339815MaRDI QIDQ2334545

Simon Becker, Rui Han, Svetlana Ya. Jitomirskaya

Publication date: 7 November 2019

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.00988

zbMATH Keywords

manifoldsgraphsspectral analysisfractalslatticeslattice systemsselfadjoint operator theory in quantum theoryIsing systemsgraphs and linear algebraPotts systemsstatistical mechanical studies of nanostructures and nanoparticlessystems on graphs arising in equilibrium statistical mechanics

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Statistical mechanics of nanostructures and nanoparticles (82D80)

Related Items (13)

On the spectrum of critical almost Mathieu operators in the rational case ⋮ Spectral decimation of a self-similar version of almost Mathieu-type operators ⋮ Magnetic oscillations in a model of graphene ⋮ Stable defect states in the continuous spectrum of bilayer graphene with magnetic field ⋮ On the magnetic Schrödinger hyperbolic equation with randomized coefficients ⋮ Trace formulas for magnetic Schrödinger operators on periodic graphs and their applications ⋮ One-dimensional quasiperiodic operators: global theory, duality, and sharp analysis of small denominators ⋮ Continuum Schrödinger operators for sharply terminated graphene-like structures ⋮ Discrete Bethe-Sommerfeld conjecture for triangular, square, and hexagonal lattices ⋮ Spectral dimension for \(\beta\)-almost periodic singular Jacobi operators and the extended Harper's model ⋮ Reducible Fermi surface for multi-layer quantum graphs including stacked graphene ⋮ Global rigidity for ultra-differentiable quasiperiodic cocycles and its spectral applications ⋮ Honeycomb structures in magnetic fields

Cites Work

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• Chambers's formula for the graphene and the Hou model with kagome periodicity and applications
• Complex one-frequency cocycles
• Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structures
• The colored Hofstadter butterfly for the honeycomb lattice
• On the measure of the spectrum for the almost Mathieu operator
• Almost localization and almost reducibility
• Cantor and band spectra for periodic quantum graphs with magnetic fields
• Spectra of Schrödinger operators on equilateral quantum graphs
• Global theory of one-frequency Schrödinger operators
• On the spectra of carbon nano-structures
• Theory of nonlinear lattices
• Zero measure spectrum for the almost Mathieu operator
• The Mourre theory for analytically fibered operators
• Quantum wires with magnetic fluxes
• Cantor spectrum for the almost Mathieu operator
• Spectral theory of extended Harper's model and a question by Erdős and Szekeres
• Analytic quasi-perodic cocycles with singularities and the Lyapunov exponent of extended Harper's model
• Perturbation theory for linear operators.
• Resonant delocalization for random Schrödinger operators on tree graphs
• The Ten Martini problem
• Magnetic oscillations in a model of graphene
• Wave packets in honeycomb structures and two-dimensional Dirac equations
• An example of unitary equivalence between self-adjoint extensions and their parameters
• An overview of periodic elliptic operators
• Dominated splittings and the spectrum of quasi-periodic Jacobi operators
• Quasitriangular Matrices
• Honeycomb Schrödinger Operators in the Strong Binding Regime
• Dry Ten Martini problem for the non-self-dual extended Harper’s model
• Absence of Point Spectrum for the Self-Dual Extended Harper’S Model
• On the low lying spectrum of the magnetic Schrödinger operator with kagome periodicity
• Cantor spectra of magnetic chain graphs
• Honeycomb lattice potentials and Dirac points
• Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs
• Surface states and spectra.

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