# Quantum quench dynamics of the attractive one-dimensional Bose gas via the coordinate Bethe ansatz

## TL;DR

This paper investigates the dynamics of an attractive one-dimensional Bose gas using the coordinate Bethe ansatz, focusing on correlation functions, solitonic states, and relaxation after a quench.

## Contribution

It applies the coordinate Bethe ansatz to analyze quench dynamics and correlation functions in the attractive Lieb-Liniger model for small particle numbers.

## Key findings

- Correlation functions near solitonic crossover are computed.
- Postquench dynamics show the influence of bound states.
- Temporal averages reveal relaxation behavior.

## Abstract

We use the coordinate Bethe ansatz to study the Lieb-Liniger model of a one-dimensional gas of bosons on a finite-sized ring interacting via an attractive delta-function potential. We calculate zero-temperature correlation functions for seven particles in the vicinity of the crossover to a localized solitonic state and study the dynamics of a system of four particles quenched to attractive interactions from the ideal-gas ground state. We determine the time evolution of correlation functions, as well as their temporal averages, and discuss the role of bound states in shaping the postquench correlations and relaxation dynamics.