Electron conduction in one-dimension

I will review the recent developments of the theories of electron transport in one-dimension and the experiments relevant to those theories. Almost all the theories on one-dimensional systems are concerned with the effects of the electron-electron interaction. We will see that the interaction effects show up in various forms depending on the structure of the system. In the pure system, a theory predicts the reduction of the conductance: absence of the reduction in the experiments is explained in terms of a proper definition of the conductance. In the presence of a potential barrier, the conductance vanishes like Tα as T → 0. This behaviour is observed experimentally in somewhat different forms. On the other hand, in a system in which a quantum dot is embedded, one observes a perfect transmission of electrons through it if the number of the electrons in the dot is odd (the Kondo effect). This phenomena is observed in a beautiful experiment. This paper is intended for those who are not experts in this field. For most problems there are several theories which give similar results. Among them, I will review the one which can be understood with the least mathematical knowledge and not necessarily the one which treated the problem for the first time. As for the experiments, I have chosen the ones in which the results are shown in the forms easily understood