We show that a 2N junction SQUID (Superconducting QUantum Interference Device) made of 2N overdamped, shunted, identical junctions may be described as a system having only 6 degrees of freedom for any N > 2. This is achieved by means of the reduction introduced by Watanabe and Strogatz (Physica D, Vol. 74, (1994) p. 197) for series biased arrays. In our case 6 rather than 3 degrees of freedom are necessary to describe the system, due to the requirement of phase quantization along the superconducting loop constituting the device. Generalization to multijunction parallel arrays is straightforward.
@article{arxiv.supr-con/9507005,
title = {Constants of motion in the dynamics of a 2N-junction SQUID},
author = {C. Nappi and G. Filatrella and S. Pagano},
journal= {arXiv preprint arXiv:supr-con/9507005},
year = {2009}
}
Comments
Figures available from the authors. Submitted to Phys. Lett. A