NONLINEAR DYNAMICS OF DRIVEN SINGLE-ELECTRON TUNNELING JUNCTIONS

In this paper we investigate the nonlinear dynamics of circuits made of single-electron tunneling junctions (SETJ) driven by a sinusoidal pump and biased by a DC voltage source. The mathematical model of an isolated SETJ circuit is a first-order nonautonomous impulsive differential equation. The tunneling effect of each SETJ can be realistically modeled by the impulsive effect of the junction voltage, which we choose to be the state variable of our circuit model. Based on this model we present theoretical results on the stability of the periodic and almost periodic solutions of driven SETJs. Our theoretical results show there are two phase states in each isolated SETJ circuit, which corresponds to two phase-shifted periodic solutions of our model. We present theoretical and numerical results of return maps of an isolated SETJ circuit. Our results also show that if the tunneling events are equipotentially almost periodic then the attractors generated by two-coupled SETJs will be confined to the vicinity of some periodic orbits. This result provides a foundation for implementing robust logic operations in nanoelectronics.