Near-hydrodynamic electron flow according to the linearized Boltzmann equation

Near-hydrodynamic electron flows have been realized in a number of recent experiments, where momentum-conserving collisions dominate the flow behavior. We analyze these flows using a matched asymptotic expansion of the governing linearized Boltzmann equation to second order in the rarefaction parameter---the Knudsen number---with arbitrary diffusely scattering boundaries. We find corrections to the bulk governing equations, boundary conditions, and near-boundary dynamics unreported in the literature. The developed theory is used to solve two-dimensional Poiseuille flow in the near-hydrodynamic regime. Nonhydrodynamic corrections are found to compete with the classical Hall or odd viscosity. Our results are in excellent agreement with high-fidelity numerical solutions of the linearized Boltzmann equation.