Superfluidity in Bose-Hubbard circuits

The essence of superfluidity is the possibility to witness metastable flow states. In the standard classical stability analysis, one finds that flow states whose rotation velocity is less than a critical velocity are metastable (“Landau criterion”). In this talk I will show that the standard superfluidity criteria fail in low-dimensional circuits and that a proper determination of the superfluidity regime-diagram requires a quantum chaos perspective. In particular, I will explain the drastic differences between three-site rings and rings that have more than three sites. In the former, instability of flow states is due to a swap of separatrices, while in the latter it has to do with a web of non-linear resonances.