An important aspect of physics today is the effort to understand how the fundamental laws of nature result in complex behavior, often referred to as the study of emergent phenomena. For example, how does something as straightforward as a system of gas molecules organize itself into something as complex as a tornado?Two factors play a key role in the study of emergent phenomena: complexity, the number of constituents in a system, and nonlinearity, a property common to most system dynamics.Nonlinear systems which can be controlled, easily measured and scaled to large numbers are thus important to understand.

Networks of superconducting Josephson junctions are examples of such systems. Josephson junctions are inherently nonlinear systems which can be fabricated with adjustable parameters, measured in a straightforward fashion, and easily scaled to large network sizes. In addition, a large circuit of Josephson junctions measured over a long time contains dynamics which would be essentially impossible to calculate on a computer, but which can be observed with basic electrical measurements.

In our research, we study the behavior of networks of Josephson junctions. We have followed previous work in this field in studying soliton-like modes called fluxons or vortices and localized modes called discrete breathers. We have also begun work on synchronization in a system of disordered oscillators. Finally, we have devised a circuit of Josephson junctions to accurately model the time-dependent behavior of the voltage of a neuron, with an eye toward studying the emergent behavior of a large, coupled neural network.

Our work fits in with Colgate University’s strong tradition of undergraduate student involvement in academic research.