Work

Quantum graphs featuring unusual self-adjoint extensions

Year: 2025

Type: article

Abstract: We present an example of a simple quantum graph with “vertices at infinity”, which appear due a strongly attractive potential making the spectral problem quantum-mechanically incomplete. We construct the appropriate self-adjoint extensions of the formal graph Hamiltonian, and derive their spectral properties.

Source: Acta Polytechnica

DOI: 10.14311/ap.2025.65.0539

Author: Pavel Exner

Institutions: Czech Academy of Sciences, Czech Academy of Sciences, Nuclear Physics Institute, 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: European Commission

Awards: Spectral Optimization: From Mathematics to Physics and Advanced Technology, G434337789