在此論文中，我們依據弱局域化效應來探討準低維無序系統的磁導性質。我們考慮了兩個系統來進行討論。其一為準一維的圓柱線，另一個是準二維的三明治結構。
就圓柱線這個題目而言，我們發展了轉移矩陣的方法來解這個問題中所遇到的微分方程式並將我們計算所得到之磁導與用微擾方法所得到的結果比較[B. L. Altshuler, A. G. Aronov, 1981a, Pis’ma Zh. Eksp. Teor. Fiz. 33, 515 [JETP Lett. 33, 499 (1981)]]。一般而言，這兩種方法所得到的結果在低溫及小磁場的情況下是一致的。在高溫及大磁場的時候兩者略有偏差。我們這個工作將圓柱線的磁導計算拓展至高溫及大磁場的情況。除此之外，我們的計算方法可以用來探討不均勻的圓柱線的磁導。
三明治結構由中間為髒的金屬薄膜與兩旁近乎絕緣的區域所構成，它的材料性質使得其古典電流傳輸主要發生在金屬層。我們針對這個系統去算它的電導量子修正(QC)及磁導(MC)。結果顯示，三明治結構在特定的材料條件下其QC/MC會在某個低溫區呈現飽和行為。此外，其QC/MC在極低溫時最後會發散。在塊材的結構中，其厚度與寬度相近，我們的分析發現其QC甚至到零溫也是飽和。相類似地，假如系統符合乾淨塊材極限，也就是電子的運動在近乎絕緣的區域是彈道的 (ballistic)，其MC在零溫也呈現飽合。我們在三明治結構的工作可以定性地解釋在準二維薄膜中所觀察到的失相時間飽合與極低溫的失相時間上升現象[S. M. Huang, T. C. Lee, H. Akimoto, K. Kono, J.-J. Lin, Phys. Rev. Lett. 99, 046601 (2007)]。這個計算可拓展至不均勻的準一維系統，也就是量子線。

In this thesis, we discuss the magneto-transport properties in quasi-low-dimensional disordered systems under weak localization theory. Two systems are considered in this work. One is the quasi-one-dimensional (Q1D) cylindrical wire, and the other is the quasi-two-dimensional (Q2D) sandwich structure.
For the cylindrical wire case, we develop a transfer-matrix method to solve the differential equation in the problem and compare our calculated magnetoconductance (MC) with the one obtained by perturbation method [B. L. Altshuler, A. G. Aronov, 1981a, Pis’ma Zh. Eksp. Teor. Fiz. 33, 515 [JETP Lett. 33, 499 (1981)]]. In general, the two results of different methods agree well with each other at low temperatures and at small magnetic fields. Slight deviations are found at high temperatures and at large magnetic fields when comparing these two results. Our work in this case extends the calculation of MC for cylindrical wire to high temperatures and large magnetic fields. In addition, our method could be applied to investigate the MC of non-uniform disordered cylindrical wires.
The sandwich structure consists of a dirty metallic film bounded by relatively clean but nearly insulating layers on the sides, with material parameters chosen so that the structure has classical current transport confined mainly in the metallic layer. Quantum correction of conductance (QC) and MC are calculated for this system. The result shows that QC/MC saturates over a range of low temperatures for a certain range of structural/material parameters of the sandwich structure. Moreover, QC/MC goes divergent at extreme low temperatures eventually. In the bulk-like limit, where the thickness of this system is comparable to its width, our analysis shows that QC saturates even down to zero temperature. Similarly, MC also shows saturation at zero temperature if the system satisfies the requirement of clean-bulk limit where electron’s motion in the nearly insulating layers is ballistic. Our work of sandwich structure could qualitatively explain the observed dephasing time saturation in Q2D films and the upturn of dephasing time at extreme low temperatures [S. M. Huang, T. C. Lee, H. Akimoto, K. Kono, J.-J. Lin, Phys. Rev. Lett. 99, 046601 (2007)]. The calculation can be extended to Q1D non-uniform disordered systems of, i.e., quantum wires.

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