# Viscous Dissipation in One-Dimensional Quantum Liquids

## TL;DR

This paper develops a theory for viscous dissipation in one-dimensional quantum liquids, revealing that bulk viscosity diverges at zero temperature and is infinite in integrable models, indicating a breakdown of hydrodynamics.

## Contribution

It provides a universal theoretical framework for understanding viscosity in 1D quantum liquids, including the divergence behavior and special cases of integrable models.

## Key findings

- Bulk viscosity diverges at zero temperature for generic interactions.
- In integrable models, viscosity is infinite at all temperatures.
- Hydrodynamic description breaks down in integrable cases.

## Abstract

We develop a theory of viscous dissipation in one-dimensional single-component quantum liquids at low temperatures. Such liquids are characterized by a single viscosity coefficient, the bulk viscosity. We show that for a generic interaction between the constituent particles this viscosity diverges in the zero-temperature limit. In the special case of integrable models, the viscosity is infinite at any temperature, which can be interpreted as a breakdown of the hydrodynamic description. Our consideration is applicable to all single-component Galilean-invariant one-dimensional quantum liquids, regardless of the statistics of the constituent particles and the interaction strength.