I. 低維半導體中的電子自旋馳豫 II. 微生物鞭毛間的流體動力交互作用

Abstract

在這篇論文中，我們主要探討兩個主題：I.低維半導體中的電子自旋馳豫 II.微生物鞭毛間的流體動力交互作用。這兩個主題分別隸屬於凝態和軟物質兩個不同的物理領域。

在主題 I 中，我們探究低維半導體 (二維電子氣) 中，基於 Elliott-Yafet 和 D'yakonov-Perel'自旋馳豫機制所導致的電子自旋馳豫現象。我們運用 Ensemble Monte Carlo (EMC) 和Semiclassical path integral (SPI) 方法來研究這些問題。藉由運用 EMC 和 SPI 這兩個方法來加以計算，我們發現其結果與一些理論推演和實驗數據互相一致。並且我們也預測出一些有趣的結果，這些發現可作為將來實驗設計的指導方針。

在主題 II 中，我們試著揭露出細菌地毯鞭毛運動的集體行為。我們提出兩個簡單模型 Microorganism-flagellum-rotor matrix (MFRmatrix) 和 Microorganism-flagellum-rotor sweep (MFRsweep) 來摹擬真實世界中複雜萬分的細菌鞭毛轉動和甩動的行為。我們使用 Blake-Oseen tensor (BOT) 來描述細菌鞭毛彼此之間和鞭毛與示蹤粒子之間的流體動力交互作用。藉由運用 MFRmatrix 和 MFRsweep 這兩個模型以及 BOT 來研究微生物鞭毛陣列的行為，我們提出一些合理的見解來解釋最近的一些實驗結果。此外我們也預測出一些有趣的現象，這些發現可作為將來實驗設計的指導方針。

In this thesis we explore two main topics: I. Spin relaxations in low dimensional semiconductors and II. Hydrodynamic interactions between microorganism flagella. These two topics belong to two different physical fields, condensed matter and soft matter fields.

In Part I, we focus on exploring the Elliott-Yafet and D'yakonov-Perel' spin relaxation mechanisms inducing electron spin relaxation in low dimensional semiconductors (two-dimensional electron gas). The main exploration approaches are Ensemble Monte Carlo (EMC) and Semiclassical path integral (SPI) methods. By utilizing these two methods, some consistent results between our study and some theoretical and experimental results are obtained. In addition our study also predicts some interesting findings which may offer as design guidance for future experiments setting up.

In Part II, we try to reveal the bacterial carpet flagella collective behavior. We propose two minimal models Microorganism-flagellum-rotor matrix (MFRmatrix) and Microorganism-flagellum-rotor sweep (MFRsweep) to mimic the real and complex bacterium flagella rotation and sweep behavior, respectively. And in order to properly describe the hydrodynamic interaction between the bacterium flagella themselves and between the bacterium flagellum and tracer particle, the hydrodynamic interaction Blake-Oseen tensor (BOT) is employed. By utilizing these two models and BOT in studying microorganism matrix, we give some reasonable explanation to account for recent experimental results. Besides, our study also predicts some interesting findings which may offer as design guidance for future experiments setting up.