Superfluidity and Swallowtails; Hysteretic Behavior in Bose Condensates

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 swallowtail 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 states due to quantum fluctuations.