# Hydrodynamic charge and heat transport on inhomogeneous curved spaces

## TL;DR

This paper develops a hydrodynamic theory for charge and heat transport in strongly interacting systems on curved spaces, highlighting the impact of spatial inhomogeneity and viscous effects, with relevance to materials like suspended graphene.

## Contribution

It introduces a novel hydrodynamic framework for inhomogeneous curved spaces, analyzing the effects of spatial curvature on transport properties in condensed matter systems.

## Key findings

- Thermal and electrical conductivities are dominated by viscous effects.
- Thermal conductivity is highly sensitive to spatial inhomogeneity.
- The theory is applicable to systems like suspended graphene at the Dirac point.

## Abstract

We develop the theory of hydrodynamic charge and heat transport in strongly interacting quasi-relativistic systems on manifolds with inhomogeneous spatial curvature. In solid-state physics, this is analogous to strain disorder in the underlying lattice. In the hydrodynamic limit, we find that the thermal and electrical conductivities are dominated by viscous effects, and that the thermal conductivity is most sensitive to this disorder. We compare the effects of inhomogeneity in the spatial metric to inhomogeneity in the chemical potential, and discuss the extent to which our hydrodynamic theory is relevant for experimentally realizable condensed matter systems, including suspended graphene at the Dirac point.