Lieb-Liniger model of a dissipation-induced Tonks-Girardeau gas
  We show that strong inelastic interactions between bosons in one dimension create a Tonks-Girardeau gas, much as in the case of elastic interactions. We derive a Markovian master equation that describes the loss caused by the inelastic collisions. This yields a loss rate equation and a dissipative Lieb-Liniger model for short times. We obtain an analytic expression for the pair correlation function in the limit of strong dissipation. Numerical calculations show how a diverging dissipation strength leads to a vanishing of the actual loss rate and renders an additional elastic part of the interaction irrelevant. 
S. D\"urr, J. J. Garcia-Ripoll, N. Syassen, D. M. Bauer, M. Lettner,   J. I. Cirac, G. Rempe