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

TL;DR

This paper derives an exact expression for the polaron mass in a one-dimensional Bose gas using the Yang-Gaudin model, providing insights into weak and strong interaction regimes.

Contribution

It presents the first exact formula for the polaron mass in a 1D Bose gas, linking it to the ground-state energy derivative and enabling high-order series expansions.

Findings

Exact polaron mass formula derived for the Yang-Gaudin model.

High-order power series for polaron mass in different interaction regimes.

Provides a theoretical foundation for understanding polaron behavior in 1D Bose gases.

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.