Synchronization in disordered superconducting arrays

This paper describes the effect of quenched disorder on the synchronization properties of a class of circuits known as Josephson junction arrays. The methodology extends the 'dynamical systems approach' used to analyze identical-element arrays to a 'statistical mechanics approach' to incorporate disorder, a topic of great importance from the perspective of device applications. The essential step is to map the circuit equations onto a version of the fabled Kuramoto model, whose tractability allows one to quantify the system-wide quality of synchronization.