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 T α 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.