## SciPost Submission Page

# The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas

### by Isabelle Bouchoule, Benjamin Doyon, Jerome Dubail

### Submission summary

As Contributors: | Isabelle Bouchoule · Jerome Dubail |

Arxiv Link: | https://arxiv.org/abs/2006.03583v1 (pdf) |

Date submitted: | 2020-06-17 |

Submitted by: | Dubail, Jerome |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Quantum Physics |

Approaches: | Theoretical, Computational |

### Abstract

We theoretically investigate the effects of atom losses in the one-dimensional (1D) Bose gas with repulsive contact interactions, a famous quantum integrable system also known as the Lieb-Liniger gas. The generic case of K-body losses (K = 1,2,3,...) is considered. We assume that the loss rate is much smaller than the rate of intrinsic relaxation of the system, so that at any time the state of the system is captured by its rapidity distribution (or, equivalently, by a Generalized Gibbs Ensemble). We give the equation governing the time evolution of the rapidity distribution and we propose a general numerical procedure to solve it. In the asymptotic regimes of vanishing repulsion -- where the gas behaves like an ideal Bose gas -- and hard-core repulsion -- where the gas is mapped to a non-interacting Fermi gas -- we derive analytic formulas. In the latter case, our analytic result shows that losses affect the rapidity distribution in a non-trivial way, the time derivative of the rapidity distribution being both non-linear and non-local in rapidity space.