"Nonlinear and Neural Dynamics in Josephson Networks"

Superconducting Josephson Junctions are one of the most active areas of research in Condensed Matter Physics today.  One unique aspect of Josephson Junctions is the nonlinear relation between the phase of the wave function and the supercurrent flowing though the junction.  This manifests itself in a nonlinear, pendulum-like equation for the dynamics of the phase when the junction is placed in circuit.  Josephson junctions 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 talk will discuss some collective, emergent behavior of Josephson junction networks.  First, we will discuss our work on soliton-like modes called fluxons, which have particle-like properties in a parallel array (1,2).  Next, we will discuss the Kuramoto-like synchronization of a system of disordered oscillators.  Finally, we will show how a circuit of Josephson junctions can be designed to accurately model the time-dependent voltage of a biological neuron (3).  This has a longer-term goal of studying the emergent behavior of a large, coupled neural network.

(1)    “Experimental observation of Fluxon Diffusion in Josephson Rings,” K. Segall, A. Dioguardi, N. Fernandes and J.J. Mazo, Journal of Low Temperature Physics 154, 41-54 (2009).
(2)    “Thermal depinning of Josephson Fluxons in superconducting rings,” J.J. Mazo, F. Naranjo and K. Segall, Physical Review B78, 174510 (2008).
(3)    “Josephson junction simulation of neurons,” P. Crotty,  D. Schult and K. Segall, Physical Review E 82, 011914 (2010).