Exact result for the polaron mass in a one-dimensional Bose gas

Abstract

We study the polaron quasiparticle in a one-dimensional Bose gas. In the integrable case described by the Yang-Gaudin model, we derive an exact result for the polaron mass in the thermodynamic limit. It is expressed in terms of the derivative with respect to the density of the ground-state energy per particle of the Bose gas without the polaron. This enables us to find high-order power series for the polaron mass in the regimes of weak and strong interaction.