2006/05/03 by Brando Bellazzini, B. Bellazzini, Mihail Mintchev +1 · 63 citations
Mathematics · Physics and Astronomy · #Algebraic number #Algebraic structures and combinatorial models #Casimir effect #Discrete mathematics #Graph #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Physics #Pure mathematics #Quantum #Quantum mechanics #Quantum optics and atomic interactions #Schrödinger's cat #Star (game theory) #Theoretical physics #Vertex (graph theory) #cond-mat.mes-hall #hep-th #math-ph #math.MP #nlin.SI #quant-ph
paper · pdf · doi:10.1088/0305-4470/39/35/011
published in Journal of Physics A Mathematical and General 39(35), 11101-11117 (Institute of Physics) · LaTex 23+1 pages, 4 figures
arxiv created 2006/05/03 · openalex publication_date 2006/08/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We construct canonical quantum fields which propagate on a star graph modelling a quantum wire. The construction uses a deformation of the algebra of canonical commutation relations, encoding the interaction in the vertex of the graph. We discuss in this framework the Casimir effect and derive the correction to the Stefan–Boltzmann law induced by the vertex interaction. We also generalize the algebraic setting in order to cover systems with integrable bulk interactions and solve the quantum nonlinear Schrödinger model on a star graph.