  We investigate the effects of a trapping space-dependent potential on the
low-temperature quasi-long-range order phase of two-dimensional particle
systems with a relevant U(1) symmetry, such as quantum atomic gases. We
characterize the universal features of the trap-size dependence using scaling
arguments. The resulting scenario is supported by numerical Monte Carlo
simulations of a classical two-dimensional XY model with a space-dependent
hopping parameter whose inhomogeneity is analogous to that arising from the
trapping potential in experiments of atomic gases.
