We present a theory of hysteretic phenomena in Bose gases, using superfluidity in one-dimensional rings and in optical lattices as primary examples. Through this study we are able to give a physical interpretation of swallow-tail loops recently found by many authors in the mean-field energy structure of trapped atomic gases. These loops are a generic sign of hysteresis, and in the present context are an indication of superfluidity. We have also calculated the rate of decay of metastable current-carrying-slates due to quantum fluctuations.
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