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Atom losses occur naturally during cold atoms experiments. Since thisphenomenon is unavoidable, it is important to understand its effect on theremaining atoms. Here we study a gas of hard-core bosons on a lattice subjectto $K$-body losses (where $K=1,2,3,\dots$ is the number of atoms lost in eachloss event), and in particular we investigate the effect of losses on therapidity distribution $\rho(k)$ of the atoms. Under the assumption that lossesare weak enough so that the system relaxes between two loss events, we are ableto determine the loss functional $F[\rho](k)$ encoding the loss process for$K$-body losses. We derive closed expressions for the cases of one- andtwo-body losses, and show their effects on the evolution of the total number ofparticles. Then we add a harmonic trapping potential and study the evolution ofthe position-dependent rapidity distribution of this system by solvingnumerically the evolution equation for one-, two- and three-body losses.

Effects of atom losses on a one-dimensional lattice gas of hardcore bosons