The electron transport inside two-dimensional nanostructure is numerically studied, by the nodal pattern analysis of the wave functions. Especially the doubly connected quantum ring(QR) structure provides us interesting features under an external electro-magnetic field. Recent experimental techniques in nanostructures is now sophisticated enough, for example, to control the electron number in a two-dimensional system. Then one of the main interests on electron transports in nanodevices is to know characteristics of a magnetoresistance. From the nodal pattern analysis, it is found that every state cannot contribute to the electron transport, when the overall shape of the device is not near integrable. We also find the wavefunctions that stick to the inner wall of the QR under a weak magnetic field. Classically such strength of magnetic field makes the cyclotron radius near the radius of the inner hole of the device. it implies that there must be the noble relation between the ring size of the inner hole and the cyclotron radius of an electron motion and the electron transport is dependent on the relation. Consequently, the resistance is affected by the drive of an ac electro-magnetic field which is capable of exciting the electron to the higher eigenstate.
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