  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.
