The exponential decay of eigenfunctions for tight-binding Hamiltonians via landscape and dual landscape functions

DOI10.1007/s00023-020-00986-2zbMath1462.81092arXiv2003.07987OpenAlexW3011773521WikidataQ114232026 ScholiaQ114232026MaRDI QIDQ2025610

Shiwen Zhang, Wei Wang

Publication date: 14 May 2021

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.07987

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) PDEs in connection with fluid mechanics (35Q35) General topics in linear spectral theory for PDEs (35P05) Estimates of eigenvalues in context of PDEs (35P15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items

Landscape approximation of the ground state eigenvalue for graphs and random hopping models ⋮ On an effective equation of the reduced Hartree-Fock theory ⋮ An Agmon estimate for Schrödinger operators on graphs ⋮ Counting eigenvalues of Schrödinger operators using the landscape function ⋮ The effective potential of an M-matrix ⋮ The landscape law for tight binding Hamiltonians

Cites Work

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• An eigensystem approach to Anderson localization
• Absence of diffusion in the Anderson tight binding model for large disorder or low energy
• Sur le spectre des opérateurs aux différences finies aléatoires
• Semi-classical analysis for the Schrödinger operator and applications
• Localization at large disorder and at extreme energies: an elementary derivation
• Localization of classical waves. I: Acoustic waves
• Localization of classical waves. II: Electromagnetic waves
• Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential
• Anderson localization for Bernoulli and other singular potentials
• Localization for one-dimensional, continuum, Bernoulli-Anderson models.
• Metal-insulator transition for the almost Mathieu operator
• Localization near the edge for the Anderson Bernoulli model on the two dimensional lattice
• Detecting localized eigenstates of linear operators
• On localization in the continuous Anderson-Bernoulli model in higher dimension
• The Landscape of Anderson Localization in a Disordered Medium
• Random Walks and Heat Kernels on Graphs
• Localization of quantum states and landscape functions
• An Invitation to Random Schroedinger operators
• Computing Spectra without Solving Eigenvalue Problems
• Localization of eigenfunctions via an effective potential
• Localization properties of the disordered XY spin chain
• Finite-volume fractional-moment criteria for Anderson localization

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