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Localization on the quantum graph connecting the points of the lattice ${\Bbb Z}^{d}$

Year: 2025

Type: article

Abstract: We consider the graph whose edges connect all nearest neighbours of the lattice \mathbb{Z}^{d} . We prove several theorems establishing localization of eigenfunctions of the Schrödinger operator on this graph. The energies for which we establish the localization belong to specific intervals whose union is an unbounded subset of the real line.

Source: Journal of Spectral Theory

DOI: 10.4171/jst/584

Authors: Stanislav Alekseevich Molchanov, Oleg Safronov

Institution: University of North Carolina at Charlotte

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4414794889

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