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.
