many works have been devoted to the study of the mesoscopic systems
because the electronic transport property in mesoscopic systems is not only a basic theoretical topic but also could benefit the design of useful electronic devices. Research on these systems revealed many novel phenomena. These phenomena
which usually appear in mesoscopic systems
are called mesoscopic phenomena. One of the mesoscopic phenomena is the persistent current flowing in a mesoscopic ring threaded by a magnetic flux. Experimental and theoretical research has shown that a magnetic flux which threads an isolated ring of mesoscopic dimensions creates persistent current. Moreover
it has been theoretically shown that in such a system self-sustaining current can still run even if the external flux is switched off. General quantum-mechanical principles require that the wave functions
eigenvalues
and hence all observable quantities should be periodic in the magnetic flux threading the loop with a period 0(0=
hc/e
being the flux quantum). It is well known that the magnetic flux destroys the time-reversal symmetry and
as a consequence
the degeneracy of the states carrying current clockwise and anticlockwise is lifted. Since the discovery of the persistent current
there have been many studies on the single ring
coupled ring
and multiple-arm ring structures. Studies show us that in the presence of a transport current
the persistent current can flow in a ring
even in the absence of a magnetic field. The purpose of this paper is to study persistent currents in the triple-arm ring coupled to two external leads by quantum waveguide theory. It is found that in the presence of a transport current
the persistent currents can flow in a triple-arm ring
even if the magnetic flux is absent and the lengths of the upper and the lower arms are equal. With different lengths of the three arms
the persistent currents in the three arms are different. Beside
the persistent currents in the triple-arm ring and the single ring are different
even though the ratios of the upper arm to the lower arm of the two rings are the same.
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