Discrete sine-Gordon equation on metric graphs: A simple model for Josephson junction networks

TL;DR

This paper studies the discrete sine-Gordon equation on branched metric graphs, providing exact solutions under certain constraints and numerical solutions otherwise, to model Josephson junction networks.

Contribution

It introduces a simple model for Josephson junction networks using discrete sine-Gordon equations on metric graphs, with analytical and numerical solutions.

Findings

Exact solutions under specific sum rule constraints

Numerical solutions when constraints are not met

Modeling of Josephson junction networks

Abstract

We consider discrete sine-Gordon equation on branched domains. The latter is modeled in terms of the metric graphs with discrete bonds having the form of the branched 1D chains. Exact analytical solutions of the problem are obtained for special case of the constraints given by in terms of simple sum rule. Numerical solution is obtained when the constraint is not fulfilled.