  We show that the direction of coherent electron transport across a cyclic
system of quantum dots or a cyclic molecule can be modulated by an external
magnetic field if the cycle has an odd number of hopping sites, but the
transport becomes completely symmetric if the number is even. These contrasting
behaviors, which remain in the case of interacting electrons, are a consequence
of the absence or presence of alternance symmetry in the system. These findings
are relevant for the design of nanocircuits based on coupled quantum dots or
molecular junctions.
