We investigate an infinite array of point interactions of the same strength in \mathbb{R} ^<i>d</i>, <i>d</i> = 2, 3, situated at vertices of a polygonal curve with a fixed edge length. We demonstrate that if the curve is not a line, but it is asymptotically straight in a suitable sense, the corresponding Hamiltonian has bound states. An example is given in which the number of these bound states can exceed any positive integer.

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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.