Quantum Fields on Star Graphs

TL;DR

This paper develops a quantum field theory framework on star graphs, modeling quantum wires with vertex interactions, and explores effects like Casimir and Stefan-Boltzmann law corrections, including solutions to integrable models.

Contribution

It introduces a novel algebraic approach to quantum fields on star graphs, incorporating vertex interactions and solving the quantum non-linear Schrödinger model in this setting.

Findings

Derived Casimir effect and Stefan-Boltzmann law corrections due to vertex interactions.

Constructed quantum fields on star graphs using deformed algebra of canonical commutation relations.

Solved the quantum non-linear Schrödinger model on a star graph.

Abstract

We construct canonical quantum fields which propagate on a star graph modeling 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 for covering systems with integrable bulk interactions and solve the quantum non-linear Schroedinger model on a star graph.