Abundance of Weyl points in semiclassical multiterminal superconducting nanostructures

We show that the quasicontinuous gapless spectrum of Andreev bound states in multiterminal semi-classical superconducting nanostructures exhibits a large number of topological singularities. We concentrate on Weyl points in a four-terminal nanostructure and compute their density and correlations in three-dimensional parameter space for a universal random matrix theory model as well as for the concrete nanostructures described by the quantum circuit theory. We mention the opportunities for experimental observation of the effect in a quasicontinuous spectrum.