if}\ m>2,\label{eq:linear_scattering_rates_charge}\end{aligned}$$ where $\gamma_{c}=2.57$ and $\eta_{c}=3.45$ (see Appendix \[sec:App\_Matrix-elements\] for more numerical values). It is also convenient to define an effective scattering time for the Vlasov term: $$\tau_{V}=\frac{2\pi^{2}\beta\hbar}{\alpha N\log\left(2\right)}.\label{eq:Vlasov_time}$$ Notice, that $\tau_{V}/\tau_{c,m}\sim1/\alpha$ is large for small $\alpha$.

In the thermal sector, there are two relevant modes. However, the $s=3$ mode is physically more important, because the vanishing of the corresponding scattering rates for the $m=0$ and $m=1$ channels indicate the conservation of energy and momentum. In the following, it is shown that the neglecting of the $s=2$ imbalance mode in the calculation of the thermal conductivity and viscosity, while significantly simplifying the analysis, does only result in a small numerical error. Therefore, for the purpose of calculating the transport coefficients, only the $s=3$ energy mode will be considered. The scattering times are then given by $\tau_{\varepsilon,m}=1/\Gamma_{m}^{3,3}$. Because of energy and momentum conservation, we have $\tau_{\varepsilon,m=0,1}\rightarrow\infty$, and for $m=2$, it is $\tau_{\varepsilon,2}=\frac{1}{\alpha^{2}}\frac{\hbar}{k_{B}T}\frac{9\zeta(3)}{3.341\cdot2\pi}$. For $m>2$ the linear approximation can be used: $$\tau_{\varepsilon,m}\approx\frac{1}{\alpha^{2}}\frac{\hbar}{k_{B}T}\frac{9\zeta(3)}{2\pi}\left(\gamma_{\varepsilon}\cdot\left|m\right|-\eta_{\varepsilon}\right)^{-1}\ m>2,\label{eq:linear_scattering_rates_energy}$$ with $\gamma_{\varepsilon}=5.18$ and $\eta_{\varepsilon}=11.3$.

Non-local transport coefficients\[subsec:Non-local-transport-coefficients\]
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The linear, non-local response of a system to external forces $\mathcal{F}\left(\mathbf{r}\right)$ is characterized by constitutive relations of the form $$\mathcal{J}\left(\mathbf{r},t\right)=\int d^{d}r'dt'\,\nu\left(\mathbf{r}-\mathbf{r}',t-t'\right)\mathcal{F}\left(\mathbf{r}',t'\right),\label{eq:non-local-constitutive}$$ where $\mathcal{J}\left(\mathbf{r},t\right)$ is a current sourced by the field $\mathcal{F}\left(\mathbf{r}',t'\right)$ 