The landscape law for tight binding Hamiltonians

DOI10.1007/s00220-022-04494-8OpenAlexW3119979724WikidataQ113906006 ScholiaQ113906006MaRDI QIDQ2099806

Wei Wang, Marcel Filoche, Douglas N. Arnold, Svitlana Mayboroda, Shiwen Zhang

Publication date: 18 November 2022

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.03282

zbMATH Keywords

integrated density of stateslocalization landscapetight binding Hamiltonians

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Random operators and equations (aspects of stochastic analysis) (60H25) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items (3)

Landscape approximation of the ground state eigenvalue for graphs and random hopping models ⋮ On an effective equation of the reduced Hartree-Fock theory ⋮ Counting eigenvalues of Schrödinger operators using the landscape function

Cites Work

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• The parabolic Anderson model. Random walk in random potential
• Bounds on the density of states for Schrödinger operators
• On three balls theorem for discrete harmonic functions
• The landscape law for the integrated density of states
• Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians
• Estimates of harmonic measure
• Discrete Bethe-Sommerfeld conjecture
• Long-time tails in the parabolic Anderson model with bounded potential
• On doubling properties for non-negative weak solutions of elliptic and parabolic PDE
• The exponential decay of eigenfunctions for tight-binding Hamiltonians via landscape and dual landscape functions
• Quantum dynamics of periodic and limit-periodic Jacobi and block Jacobi matrices with applications to some quantum many body problems
• Random Walks and Heat Kernels on Graphs
• The uncertainty principle
• On the Solution of Poisson's Difference Equation
• An Invitation to Random Schroedinger operators
• Interior Maximum Norm Estimates for Finite Element Methods
• Computing Spectra without Solving Eigenvalue Problems
• Localization of eigenfunctions via an effective potential
• Probability Inequalities for Sums of Bounded Random Variables
• Stability estimates for discrete harmonic functions on product domains

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