The landscape law for tight binding Hamiltonians

Abstract

The present paper extends the landscape theory pioneered in [FM, ADFJM2, DFM] to the tight-binding Schrödinger operator on ${\mathbb{Z}}^d$. In particular, we establish upper and lower bounds for the integrated density of states in terms of the counting function based upon the localization landscape.

References in corpus (3)

• Quantum Dynamics of Periodic and Limit-Periodic Jacobi and Block Jacobi Matrices with Applications to Some Quantum Many Body Problems
• The exponential decay of eigenfunctions for tight binding Hamiltonians via landscape and dual landscape functions
• Sharp estimates for the integrated density of states in Anderson tight-binding models

Cited by in corpus (2)

• Applications of the landscape function for Schrödinger operators with singular potentials and irregular magnetic fields
• Landscape approximation of the ground state eigenvalue for graphs and random hopping models