Novel phenomena in arrays of Josephson junctions

A theoretical study of the use of entropy in information studies is made and some measures of entanglement examined. A two quantum bit Hamiltonian is looked at and its general form elucidated upon with respect to the density matrix and hence the concurrence of the system as a whole. This Hamiltonian gives a general form that can be extended to a number of physical systems including those based upon superconducting electronics involving Josephson junctions. Josephson junction arrays, involving odd numbers of specialised junctions that introduce a phase shift into a ring of neighbouring normal junctions, are found to exhibit distinctive fractal patterns in the characteristics of the system. Additionally, linear arrays of normal Josephson junctions in a transmission line geometry are found to show fractal spectral patterns in the phase and energy distributions of the Josephson junction chain. New features such as a vortex-anti-vortex glass are found. The Josephson vortex glass arises without any disorder and is associated with the high energy barriers that the energy landscape is composed of. The stable configurations of the vortices and anti-vortices are the source of the fractal features that we see. The theories that we have developed for the Josephson junction arrays can be extended to other systems with similar characteristics, e.g. magnetic particles.