# Two-fluid dynamics of one-dimensional quantum liquids in the absence of Galilean invariance

## TL;DR

This paper develops a two-fluid hydrodynamic theory for one-dimensional quantum liquids lacking Galilean invariance, revealing new transport coefficients linked to backscattering, and extends the understanding of superfluid properties in realistic systems.

## Contribution

It introduces a novel two-fluid hydrodynamic framework applicable to non-Galilean-invariant quantum liquids, including explicit expressions for new transport coefficients.

## Key findings

- The theory reduces to single-fluid hydrodynamics at low frequencies.
- Three new transport coefficients arise due to broken Galilean invariance.
- Transport coefficients are expressed in terms of backscattering rate.

## Abstract

Luttinger liquid theory of one-dimensional quantum systems ignores exponentially weak backscattering of particles. This endows Luttinger liquids with superfluid properties. The corresponding two-fluid hydrodynamic description available at present applies only to Galilean-invariant systems, whereas most experimental realizations of one-dimensional quantum liquids lack Galilean invariance. Here we develop the two-fluid theory of such quantum liquids. In the low-frequency limit the theory reduces to single-fluid hydrodynamics. However, the absence of Galilean invariance brings about three new transport coefficients. We obtain expressions for these coefficients in terms of the backscattering rate.