Circuit model of ballistic multiterminal Josephson junctions

18 pages, 8 figures, supplemental material as ancillary file (7 pages, 3 figures)Nonequilibrium multiterminal superconducting devices have focused considerable interest recently in connection with Floquet theory and/or nontrivial topology. Here, we consider ballistic multiterminal Josephson junctions having length scales intermediate between the short- and long-junction limits, taking the example of four terminals. We propose a phenomenological circuit model for the quartets, that relies on nonlocal ballistic Andreev resonances within the superconducting gap, and on relaxation in the nonproximitized regions of the ballistic metal. The interplay between nonlocal two-Cooper pair resonances and relaxation produces anomalously large quartet current at low-bias voltage within a two-node model. Gating away from particle-hole symmetry favors "absence of inversion" followed by "inversion" as the bias voltage increases, where "inversion" refers to the counterintuitive larger critical current at half flux-quantum than in zero field. The model is qualitatively compatible with the recent Harvard group experiment on graphene-based four-terminal Josephson junctions