Quantum field theory on quantum graphs and application to their conductance

TL;DR

This paper develops a bosonic quantum field framework on quantum graphs, enabling the calculation of scattering matrices and conductance, with applications to condensed matter physics and validation through exact solutions.

Contribution

It introduces a new quantum field construction on quantum graphs and demonstrates its use in calculating scattering matrices and conductance, extending previous approaches.

Findings

Scattering matrix matches previous generalized star product results.

Conductance calculations are validated against exact solutions.

Framework generalizes existing models in mathematical and condensed matter physics.

Abstract

We construct a bosonic quantum field on a general quantum graph. Consistency of the construction leads to the calculation of the total scattering matrix of the graph. This matrix is equivalent to the one already proposed using generalized star product approach. We give several examples and show how they generalize some of the scattering matrices computed in the mathematical or condensed matter physics litterature. Then, we apply the construction for the calculation of the conductance of graphs, within a small distance approximation. The consistency of the approximation is proved by direct comparison with the exact calculation for the `tadpole' graph.