The thermal jitter of transmission of magnetic flux quanta in long Josephson junctions is studied. While for large-to-critical damping and small values of bias current the physically obvious dependence of the jitter versus length $sigmasimsqrt{L}$ is
confirmed, for small damping starting from the experimentally relevant $alpha=0.03$ and below strong deviation from $sigmasimsqrt{L}$ is observed, up to nearly complete independence of the jitter versus length, which is exciting from fundamental point of view, but also intriguing from the point of view of possible applications.
We present the analysis of the mean switching time and its standard deviation of short overdamped Josephson junctions, driven by a direct current and a periodic signal. The effect of noise enhanced stability is investigated. It is shown that fluctuat
ions may both decrease and increase the switching time.
