We consider resonant vortices around nodal points of the wave function describing electron transport through a mesoscopic device. With a suitable choice of the device geometry, the dominating role is played by single vortices with a preferred orientation. To characterize the strength of the resulting magnetic moment, we have introduced a magnetance, the quantity defined in analogy with the device conductance. Its basic properties and possible experimental detection are discussed.

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We study bound states of the two-dimensional Helmholtz equations with Dirichlet boundary conditions in an open geometry given by two straight leads of the same width which cross at an angle . Such a four-terminal junction with a tunable can realized experimentally if a right-angle structure is filled by a ferrite. It is known that for = 90 there is one proper bound state and one eigenvalue embedded in the continuum. We show that the number of eigenvalues becomes larger with increasing asymmetry and the bound-state energies are increasing as functions of in the interval (0, 90). Moreover, states which are sufficiently strongly bound exist in pairs with a small energy difference and opposite parities. Finally, we discuss how the bound states transform with increasing into quasibound states with a complex wave vector.