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Stationary Josephson effect in a short multi-terminal junction

We study the dc Josephson effect and the density of states in a multiterminal structure of cross-type geometry which consists of four superconducting electrodes connected by one-dimensional normal or ferromagnetic wires. We find that the Josephson current $I_{Jz}$ has a sinusoidal dependence on the phase difference $ϕ_z$ between the superconductors in the horizontal wire with a critical current $I_c$ that can be varied by changing the phase difference $ϕ_y$ between the superconductors in the vertical wire. The period of the function $I_{Jz}(ϕ_z)$ depends on the ratio of the interface resistances $R_{Sn,z}/R_{Sn,y}$ being equal to $2π$ if this ratio is small and equal to $4π$ in the opposite limit. We also calculate the amplitudes of both the singlet and the odd-frequency triplet component in the system under consideration. The triplet component amplitude may be significantly larger than the amplitude of the singlet component.