In recent years

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.