# Drude Weight for the Lieb-Liniger Bose Gas

## TL;DR

This paper derives a concise formula for the Drude weight in the Lieb-Liniger Bose gas using hydrodynamic projections, linking it to thermodynamic Bethe ansatz quantities, and provides related correlation functions.

## Contribution

It introduces a new, compact formula for the Drude weight in the Lieb-Liniger model, applicable to general linear combinations of conserved charges, and extends to dynamical correlation functions.

## Key findings

- Derived a formula for the Drude weight from thermodynamic Bethe ansatz
- Obtained dynamical charge and current correlation functions
- Provided the scaled covariance matrix of charge transfer

## Abstract

Based on the method of hydrodynamic projections we derive a concise formula for the Drude weight of the repulsive Lieb-Liniger $\delta$-Bose gas. Our formula contains only quantities which are obtainable from the thermodynamic Bethe ansatz. The Drude weight is an infinite-dimensional matrix, or bilinear functional: it is bilinear in the currents, and each current may refer to a general linear combination of the conserved charges of the model. As a by-product we obtain the dynamical two-point correlation functions involving charge and current densities at small wavelengths and long times, and in addition the scaled covariance matrix of charge transfer. We expect that our formulas extend to other integrable quantum models.