Continuum limit of the lattice quantum graph Hamiltonian

Abstract

We consider the quantum graph Hamiltonian on the square lattice in Euclidean space, and we show that the spectrum of the Hamiltonian converges to the corresponding Schrödinger operator on the Euclidean space in the continuum limit, and that the corresponding eigenfunctions and eigenprojections also converge in some sense. We employ the discrete Schrödinger operator as the intermediate operator, and we use a recent result by the second and third author on the continuum limit of the discrete Schrödinger operator.

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Cited by in corpus (3)

• Continuum limit for a discrete Hodge-Dirac operator on square lattices
• Discrete approximations to Dirichlet and Neumann Laplacians on a half-space and norm resolvent convergence
• Continuum limit for Laplace and Elliptic operators on lattices