Theory of the current-voltage characteristics of SNS junctions and other superconducting weak links

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Abstract
A theory of the current-voltage characteristics of superconducting-normal-superconducting junctions is proposed. The theory is based on a simple model current-density equation. The form of the currentvoltage characteristic is found to depend critically on whether the electrical source should be treated as a current source or a voltage source at high frequencies. A picture is given of the dynamical state of a junction at finite voltage, and all the important differences between the characteristics observed for SNS junctions and tunnel junctions are explained at least qualitatively. In particular, the theory covers the cases of a junction wide enough to be limited by its own field and the step structure known to be induced by an applied h.f. field. For wide junctions the predicted behaviour is an exactly calculable quantized flux flow in one dimension. It is the phase-locking of this flux flow by the applied h.f. field which leads to the step structure. A detailed calculation of the rounding of the steps by noise is given; the steps are predicted to be exceedingly steep. The theory is compared with the theories of other superconducting weak links.