  Experiments on collisions of isolated electrons guided along the edges in
quantum Hall setups can mimic mixing of photons with the important distinction
that electrons are charged fermions. In the so-called electronic Hong-Ou-Mandel
(HOM) setup uncorrelated pairs of electrons are injected towards a
beamsplitter. If the two electron wave packets were identical, Fermi statistics
would force the electrons to scatter to different detectors, yet this quantum
antibunching may be confounded by Coulomb repulsion. Here we model an
electronic HOM experiment using a quadratic 2D saddle point potential for the
beamsplitter and unscreened Coulomb interaction between the two injected
electrons subjected to a strong out-of-plane magnetic field. We show that
classical equations of motion for the drift dynamics of electrons' guiding
centers take on the form of Hamilton equations for canonically conjugated
variables subject to the saddle point potential and the Coulomb potential where
the dynamics of the center-of-mass coordinate and the relative coordinate
separate. We use these equations to determine collision outcomes in terms of a
few experimentally tuneable parameters: the initial energies of the
uncorrelated electrons, relative time delay of injection and the shape of the
saddle point potential. A universal phase diagram of deterministic bunching and
antibunching scattering outcomes is presented with a single energy scale
characterizing the increase of the effective barrier height due to interaction
of coincident electrons. We suggest clear-cut experimental strategies to detect
the predicted effects and give analytical estimates of conditions when the
classical dynamics is expected to dominate over quantum effects.
