Electronic Transport Properties For A Two-Channel Luttinger Quantum Wire

Strongly correlation and disorder are the two main important fundamental problems in condensed matter physics. Strongly correlation is dependent on not only the carrier interactions but also the carrier concentration. The electronic transport properties of mesoscopic systems (such as quantum wire, nanowire or quantum dot) have been paid much attention. These properties are not only important basic problems of physics but also have potential applications in the future. The quantum wire and quantum dot etc., will be very important parts of the nanocircuit. In this thesis, we study the transport properties of a clean two-channel interacting quantum wire. And some interesting new results have been predicated for the system.The thesis consists of five chapters. In chapter one we briefly introduce the both history and present of the area of interacting electrons in quantum well (or two-dimensional electron gas) of zinc-blend semiconductor heterojunction microstructures. In chapter two, an introduction to the basic steps towards the general concept of Luttinger liquid are presented in an historical order. We also introduce the hallmark features of the Luttinger liquid and some physical systems that are believed to be described by Luttinger model. Chapter three introduces the Bosonization method in detail, and the action functional of single channel quantum wire is obtained.The content of chapter four is mainly our work. We investigate theoretically the ac conductivity of a clean two-channel spinless quantum wire in\the presence of both short-ranged intra- and inter-channel electron-electron interactions which is different from other works in the past. The obtained expression of ac conductivity for the system is an oscillation function of the interaction strength, the driving frequency as well as the measured position in the wire. And the dc conductivity of the system with inter-channel interactions is smaller than that without inter-channel interactions.In chapter five a summary of the work and a outlook of this aspect are given.