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We present results of numerical simulations of the 3+1 dimensional Nambu -Jona-Lasinio (NJL) model with a non-zero baryon density enforced via theintroduction of a chemical potential mu not equal to 0. The triviality of themodel with a number of dimensions d>=4 is dealt with by fitting low energyconstants, calculated analytically in the large number of colors (Hartree)limit, to phenomenological values. Non-perturbative measurements of local orderparameters for superfluidity and their related susceptibilities show that, incontrast to the 2+1 dimensional model, the ground-state at high chemicalpotential and low temperature is that of a traditional BCS superfluid. Thisconclusion is supported by the direct observation of a gap in the dispersionrelation for 0.5<=(mu a)<=0.85, which at (mu a)=0.8 is found to be roughly 15%the size of the vacuum fermion mass. We also present results of an initialinvestigation of the stability of the BCS phase against thermal fluctuations.Finally, we discuss the effect of splitting the Fermi surfaces of the pairingpartners by the introduction of a non-zero isospin chemical potential.Comment: 41 pages, 19 figures, uses axodraw.sty, v2: minor typographical  correction

Numerical portrait of a relativistic BCS gapped superfluid