We obtain exact analytical expressions for the electronic transport through a multi-channel system, also with an applied magnetic field. The geometrical structure of the electrodes is found to cause a splitting of the conduction band into many subbands, depending on the number and the length of the chains and the conductance approaches zero when the chain number is sufficiently large, due to quantum interference. In the presence of a magnetic field a very complicated oscillatory behavior of the conductance is found with a very sensitive dependence on the number of chains and their lengths, in a remarkable distinction from the usual oscillations in two-channel Aharonov-Bohm (AB) rings. In the multi-channel system the obtained oscillation patterns and their periodicities depend on the partitioning of the magnetic flux in the areas enclosed by the electronic paths. The present study may provide a useful information for quantum dots with a special configuration.
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