  A theory is offered for a novel device, mesoscopic four-terminal SQUID. The
studied system consists of a mesoscopic four-terminal junction, one pair of
terminals of which is incorporated in a superconducting ring and the other one
is connected with a transport circuit. The nonlocal weak coupling between the
terminals leads to effects of phase dragging and magnetic flux transfer. The
behaviour of a four-terminal SQUID, controlled by the external parameters, the
applied magnetic flux and the transport current is investigated. The critical
current and the current voltage characteristics as functions of magnetic flux
are calculated. In the nonlocal mesoscopic case they depend not only on the
magnitude of the applied flux but also on its sign, allowing measurement of the
direction of the external magnetic field.
