the kinetic equation in the subspace of collinear zero modes is block diagonal in the $s=1$ and $s=2,3$ modes, as can be seen from Eqs. (\[eq:Collision\_operator\]), (\[eq:Liouville\_projected\]), (\[eq:electric\_force\_projected\])-(\[eq:viscous\_projected\]). In the following this will further simplify the calculation of transport coefficients.

Another important consequence of the linear graphene spectrum is that the heat current $\mathbf{j}_{\varepsilon}$ is proportional to the momentum density $\mathbf{g}=\sum_{\lambda}\int_{k}\hbar\mathbf{k}f_{\mathbf{k},\lambda}$ and is therefore conserved. The charge current, unlike in Galilean invariant systems, is not conserved, and decays due to interactions, giving rise to a finite restistvity in the clean system.

Scattering times\[subsec:Scattering-times\]
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The matrix elements of the collision operator determine the scattering rates of the three collinear zero modes in different angular harmonic channels. In the absence of spatial inhomogeneities and external forces, the kinetic equation in the basis of collinear zero modes (\[eq:Collinear\_modes\]) reads $$\sum_{s'}\left(\partial_{t}\delta_{s,s'}+\Gamma_{m}^{s,s'}\right)a_{m,s'}=0,\label{eq:Decay_eq}$$ where the $a_{m,s}$ are the coefficients of the expansion (\[eq:Distr\_dunction\_expanded\]). Posed as an initial value problem, this equation describes the exponential decay of collinear zero modes. This decay governs the behavior of the system at long time scales, because modes that do not set the collinear part of the collision integral to zero decay faster by a factor $\log\left(1/\alpha\right)$ (see Eq. (\[eq:Collinear\_non\_collinear\_separation\])).

