Non-quantum liquefaction of coherent gases

We show that a gas-to-liquid phase transition at zero temperature may occur in a coherent gas of bosons in the presence of competing nonlinear effects. This situation can take place both in atomic systems like Bose-Einstein Condensates in alkalii gases with two and three-body interactions of opposite signs, as well as in laser beams which propagate through optical media with Kerr (focusing) and higher order (defocusing) nonlinear responses. The liquefaction process takes place in absence of any quantum effect and can be formulated in the frame of a mean field theory, in terms of the minimization of a thermodynamic potential. We also show numerically that the effect of linear gain and three-body recombination also provides a rich dynamics with the emergence of self-organization behaviour.