Numerical portrait of a relativistic thin film BCS superfluid

We present results of numerical simulations of the (2 + 1) D Nambu-Jona-Lasinio model with a nonzero baryon chemical potential mu, including the effects of a diquark source term. Diquark condensates, susceptibilities and masses are measured as functions of source strength j. The results suggest that diquark condensation does not take place in the high density phase mu > mu(c), but rather that the condensate scales nonanalytically with j, implying a line of critical points and long range phase coherence. Analogies are drawn with the low temperature phase of the 2D XY model. The spectrum of the spin-1/2 sector is also studied, yielding the quasiparticle dispersion relation. There is no evidence for a nonzero gap; rather the results are characteristic of a normal Fermi liquid with Fermi velocity less than that of light. We conjecture that the high density phase of the model describes a relativistic gapless thin film BCS superfluid.