Fast Algorithms For Josephson Junction Arrays : Bus--bars and Defects

TL;DR

This paper reviews and extends fast numerical algorithms for 2D Josephson junction arrays, incorporating bus-bars and defects, and clarifies the influence of boundaries and gauge choices on the Green's function.

Contribution

It introduces extended algorithms for arrays with bus-bars and defects, and clarifies boundary and gauge effects on the Green's function.

Findings

Algorithms effectively model arrays with defects and bus-bars.

Green's function approach is adaptable to various boundary conditions.

Clarifies the role of gauge choice in system analysis.

Abstract

We critically review the fast algorithms for the numerical study of two--dimensional Josephson junction arrays and develop the analogy of such systems with electrostatics. We extend these procedures to arrays with bus--bars and defects in the form of missing bonds. The role of boundaries and of the guage choice in determing the Green's function of the system is clarified. The extension of the Green's function approach to other situations is also discussed.