Discrete-to-continuum convergence of the density of states for Mathieu's equation

Published 12 Dec 2025 in math.NA, math-ph, math.AP, and math.SP | (2512.12039v1)

Abstract: The density of states of a self-adjoint operator generalizes the eigenvalue distribution of a Hermitian matrix. We prove convergence of the density of states for a tight-binding model with a slowly-varying periodic potential to the density of states of its continuum approximation, a Mathieu-type equation.

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