Josephson weak links: shunted-junction and mechanical-model results

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Abstract
We have investigated two models of a superconducting weak link which give physical insight into the behavior of many Josephson-effect devices. The first of these is a low-inductance oxide-barrier Josephson tunnel junction with an external resistive shunt; the second is a mechanical analog—a driven damped pendulum. The externally shunted junction acts as a generalized weak link in that, by adjusting its shunt resistance or critical supercurrent, it exactly replicates the dc electrical characteristics of many widely different weak links. In fact, we can readily alter its characteristic while the junction is immersed in liquid helium simply by applying a small external magnetic field of 1 Oe or less to decrease the critical current. The mechanical analog, by enabling us to observe the instantaneous behavior of the phase, gives new insight into the nonlinear properties of such weak links. The behavior of both models is governed by the second-order nonlinear differential equation independently proposed by Stewart and McCumber. These models not only verify the computer-generated solutions for weak links in detail, they give new physical insight into the underlying nonlinear behavior.

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