fluid, and the flow becomes highly non-local. A very similar situation occurs when the system is subjected to spatially modulated force fields, e.g. an electric field of the form $E_{\mathbf{q}}=E_{0}e^{i\mathbf{q}\cdot\mathbf{x}}e^{-i\omega t}$ (see Fig. \[fig:Charge-and-energy\_currents\]). The response of the fluid is then determined by a non-local conductivity tensor $\sigma_{\alpha\beta}\left(\mathbf{q},\omega\right)$. An important example that is treated in Sec \[sec:Surface-acoustic-waves\] are surface acoustic waves (SAWs) in piezoelectric materials, which produce spatially modulated electric fields and can be used to study the longitudinal part of the non-local charge conductivity.

![Charge (upper row) and energy currents (lower row) excited by wavelike longitudinal electric fields and temperature differences.\[fig:Charge-and-energy\_currents\]](Pics/Non_local_transport/Longitudinal_cond_visualization_2)

main results
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In this paper, we focus on the non-local transport properties and collective excitations of graphene electrons at the charge neutrality point - prime example for a Dirac fluid. The quantum Boltzmann method developed in Ref. [@Fritz2008] is used. This method relies on the fact, that at low temperatures the graphene fine structure constant $\alpha$ is renormalized to small values. Thermally excited electrons and holes therefore appear as sharply-defined quasiparticles, whose transport properties can be studied by means of a kinetic equation. The solution of this equation is facilitated by the presence of so-called collinear modes, 