Approximating the ground state eigenvalue via the effective potential

DOI10.1088/1361-6544/ac692azbMath1491.82011arXiv2107.04969OpenAlexW3179370903MaRDI QIDQ5865784

Shiwen Zhang, Ilias Chenn, Wei Wang

Publication date: 10 June 2022

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.04969

zbMATH Keywords

Anderson modelSchrödinger operatoreffective potentialeigenvalues approximation

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Schrödinger operator, Schrödinger equation (35J10)

Related Items (3)

Landscape approximation of the ground state eigenvalue for graphs and random hopping models ⋮ Principal eigenvalue and landscape function of the Anderson model on a large box ⋮ Counting eigenvalues of Schrödinger operators using the landscape function

Cites Work

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• Ground state energy of the one-dimensional discrete random Schrödinger operator with Bernoulli potential
• Localization for one-dimensional, continuum, Bernoulli-Anderson models.
• \(L_\infty\)-estimates for the torsion function and \(L_{\infty}\)-growth of semigroups satisfying Gaussian bounds
• Computing Spectra without Solving Eigenvalue Problems
• Localization of eigenfunctions via an effective potential
• Probability Inequalities for Sums of Bounded Random Variables
• Hardy inequality and L ^p estimates for the torsion function

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