---
abstract: 'We study the response of a Dirac fluid to electric fields and thermal gradients at finite wave-numbers and frequencies in the hydrodynamic regime. We find that non-local transport in the hydrodynamic regime is governed by infinite set of kinetic modes that describe non-collinear scattering events in different angular harmonic channels. The scattering rates of these modes $\tau_{m}^{-1}$ increase as $\left|m\right|$, where $m$ labels the angular harmonics. In an earlier publication, we pointed out that this dependence leads to anomalous, Lévy-flight-like phase space diffusion [@Kiselev2019b]. Here, we show how this surprisingly simple, non-analytic dependence allows us to obtain exact expressions for the non-local heat and charge conductivities. The peculiar dependence of the scattering rates on $m$ also leads to a non-trivial structure of collective excitations: Besides the well known plasmon, second sound and diffusive modes, we find non-degenerate damped modes corresponding to excitations of higher angular harmonics. We use these results to investigate the transport of a Dirac fluid through Poiseuille-type geometries of different widths, and to study the response to surface acoustic waves in graphene-piezoelectric devices.'
author:
- 'Egor I. Kiselev'
- Jörg Schmalian
bibliography:
- 'References.bib'
title: 'Non-local hydrodynamic transport and collective excitations in Dirac fluids'
---

