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

Abstract

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

23 pages, v2: references added plus minor changes

References in corpus (10)

• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• From Interacting Particles to Equilibrium Statistical Ensembles
• Kardar-Parisi-Zhang universality from soft gauge modes
• The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
• Failure of the Generalized Eigenstate Thermalization Hypothesis in integrable models with multiple particle species
• Quantum quenches and Generalized Gibbs Ensemble in a Bethe Ansatz solvable lattice model of interacting bosons
• Breakdown of Tan's relation in lossy one-dimensional Bose gases
• Three-body local correlation function in the Lieb-Liniger model: bosonization approach
• Generalized Gibbs Ensemble and string-charge relations in nested Bethe Ansatz