Josephson tunnel junction time-dependence calculations based on the Bardeen-Cooper-Schrieffer theory

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Abstract
The feasibility and the importance of using the full BCS theory for numerical calculations of the time‐dependent behavior of a Josephson tunnel junction is examined by investigating switching from the zero to the finite voltage state. The calculation can be done, but only if the RC time constant is not too long. The results differ appreciably from those obtained with the crude but frequently used ’’resistively shunted junction’’ model. Artifical rounding of the energy‐gap edge, in the form of ’’memory reduction,’’ is introduced and shown to reduce computational difficulties appreciably without significantly altering any results. This should make many more situations amenable to accurate digital simulation.