In ultra-high quality two-dimensional (2D) materials the mean free paths of phonons and electrons relative to all mechanisms of scattering can be much greater than a size of a sample. In this case the most intensive type of scattering of particles is their collisions with sample edges and the ballistic regime of heat and charge transport is realized. We study the ballistic transport of classical interacting 2D particles in a long narrow sample. We show that the inter-particle scattering conserving momentum leads to a positive hydrodynamic correction to the ballistic conductance, which is a precursor of the viscous Poiseuille flow. We examine the effect of weak magnetic field on the electron ballistic conductance and predict a novel classical ballistic mechanism for negative magnetoresistance. Our analysis demonstrates that, apparently, such mechanism explains the temperature-independent part of the giant negative magnetoresistance recently observed in the ultra-high mobility GaAs quantum wells.
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