Integrability breaking in the one-dimensional Bose gas: Atomic losses and energy loss

The one dimensional $\delta$-function interacting Bose gas (the Lieb-Liniger model) is an integrable system, which can model experiments with ultra cold atoms in traps. Even though the integrable, integrability breaking effects are always present real world experiments. In this work we consider due to atomic loss, most relevant effect We set up a framework for exact computation of losses canonical charges model, and compute result energy loss local $K$-body processes, valid arbitrary $K$. Our takes form multiple integrals, explicitly factorized experimentally cases $K=1,2,3$.