  The hallmark of superfluidity is the appearance of "vortex states" carrying a
quantized metastable circulating current. Considering a unidirectional flow of
particles in a ring, at first it appears that any amount of scattering will
randomize the velocity, as in the Drude model, and eventually the ergodic
steady state will be characterized by a vanishingly small fluctuating current.
However, Landau and followers have shown that this is not always the case. If
elementary excitations (e.g. phonons) have higher velocity than that of the
flow, simple kinematic considerations imply metastability of the vortex state:
the energy of the motion cannot dissipate into phonons. On the other hand if
this Landau criterion is violated the circulating current can decay. Below we
show that the standard Landau and Bogoliubov superfluidity criteria fail in
low-dimensional circuits. Proper determination of the superfluidity
regime-diagram must account for the crucial role of chaos, an ingredient
missing from the conventional stability analysis. Accordingly, we find novel
types of superfluidity, associated with irregular or chaotic or breathing
vortex states.
