  Infinite densities can describe the long-time properties of systems when
ergodicity is broken and the equilibrium Boltzmann-Gibbs distribution fails. We
here perform semiclassical Monte Carlo simulations of cold atoms in dissipative
optical lattices with realistic parameters. We show that the momentum infinite
density, as well as its scale invariance, should be observable in shallow
potentials. We further evaluate the momentum autocorrelation function in the
stationary and aging regime.
