  The low-temperature properties of the two-dimensional attractive Hubbard
model are strongly influenced by the fermion density. Away from half-filling,
there is a finite-temperature transition to a phase with s-wave pairing order.
However, the critical temperature is suppressed to zero at half-filling, where
long-range charge-density-wave order also appears, degenerate with
superconductivity. This paper presents Determinant Quantum Monte Carlo
simulations of the attractive Hubbard model in the presence of a confining
potential V which makes the fermion density \rho{} inhomogeneous across the
lattice. Pair correlations are shown to be large at low temperatures in regions
of the trapped system with incommensurate filling, and to exhibit a minimum as
the local density \rho(i) passes through one fermion per site. In this ring of
\rho=1, charge order is enhanced. A comparison is made between treating V
within the local-density approximation (LDA) and in an ab initio manner. It is
argued that certain sharp features of the LDA result at integer filling do not
survive the proximity of doped sites. The critical temperature of confined
systems of fixed characteristic density is estimated.
