RUI: Nonlinear and Neural Dynamics in Josephson Networks

Colgate University, Hamilton NY

Investigators

Abstract

****Technical abstract**** This individual investigator award supports an experimental and computational study of nonlinear dynamics in networks of superconducting Josephson junctions. Josephson junctions are examples of 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 Josephson junction circuit measured over a long time contains dynamics which would essentially be impossible to calculate on a computer, but which can be observed with electrical measurements. This project will take a multi-faceted approach to studying the collective, emergent behavior of Josephson junction networks. First, it will follow previous work in the field on soliton-like modes called fluxons and localized modes called discrete breathers. Next, studies will be performed on the synchronization of a system of disordered oscillators. Finally, a circuit of Josephson junctions designed to accurately model the time-dependent voltage of a biological neuron will be fabricated and tested. This has a longer-term goal of studying the emergent behavior of a large, coupled neural network. ****Non-technical abstract**** An important aspect of physics today is the effort to understand how the fundamental laws of nature result in complex behavior. For example, consider a system of gas molecules. Simple laws of force and momentum govern their collisions. With only a few molecules, the system is simple and uninteresting. With a large number of molecules, however, the system can organize itself into something complex, like a tornado. This new behavior comes about not because of a change in the fundamental laws, but rather a change in the number of constituents, in this case gas molecules, of the system. In this research, a simple electrical circuit element known as a Josephson junction is studied. Josephson junctions are made from superconducting metals and work at very low temperatures. Past experiments have looked at the behavior of a single Josephson junction and found it capable of interesting electrical behavior. However, circuits composed of large numbers of Josephson junctions have yet to be fully studied. Just like the case of gas molecules, new collective behaviors result when the number of constituents is increased. This project will look at several of these new behaviors. One of these, like a tornado, is a swirl of electrical current. Another is a collective voltage oscillation, a back and forth motion like pendulums swinging together. A final behavior is voltage spiking, similar to the on-off firing of a biological neuron. With this last behavior, a longer term goal is to build circuits which would emulate collective behaviors in the human brain, where large numbers of neurons are connected together. This project incorporates undergraduate students as the primary researchers, preparing them for technical careers in the sciences.