Re-examination of electronic transports through a quantum wire coupled to a quantum dot

In this paper we re-examine the problem of electronic transports through a system consisting of a quantum dot which has well-defined discrete energy levels connected to an infinite quantum wire, using the bosonization method and phase shift representation, we show that all previously known results can be obtained through our method in a very simple way. Furthermore, the evolution of the system from ultraviolet to infrared critical fixed points appears naturally our method.