Work

On the ground state of lattice Schrödinger operators

Year: 2025

Type: article

Abstract: We prove necessary and sufficient conditions for lattice Schrödinger operators to have a zero-energy bound state in arbitrary dimension. The two criteria are sharp, complementary, and depend crucially on both the dimension and asymptotic behaviour of the potential. The method relies on a discrete variant of Agmon’s comparison principle which is also proven. Our results represent a discrete variant of the recent criteria obtained in the continuous setting by D. Hundertmark, M. Jex, and M. Lange [Forum Math. Sigma 11 (2023), artile no. e61].

Source: Journal of Spectral Theory

DOI: 10.4171/jst/558

Authors: Michal Jex, František Štampach

Institution: Czech Technical University in Prague

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Grantová Agentura České Republiky

Awards: G12500569, G2371517770, New challenges for spectral theory: geometry, advanced materials and complex fields, G4131035492