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研究生: 林彥廷
Lin, Yen-Ting
論文名稱: 鳥類地磁感應的磁場控制及其在化學羅盤之應用
Magnetic Control of Bird's Magnetoreception and Its Application to Chemical Compass
指導教授: 楊憲東
Yang, Ciann-Dong
學位類別: 碩士
Master
系所名稱: 工學院 - 航空太空工程學系
Department of Aeronautics & Astronautics
論文出版年: 2015
畢業學年度: 103
語文別: 中文
論文頁數: 109
中文關鍵詞: 自由基對機制鳥類磁感候鳥導航量子控制磁感化學羅盤
外文關鍵詞: radical pair mechanism, quantum control, magnetoreception chemical compass
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  • 鳥類遷徙行為是一種隨著季節變化有規律的活動,方向確定和長距離的移動是這種行為的特性,研究人員對於這種精確的移動行為很感興趣,由鳥類的行為實驗的觀察,鳥類導航所利用的方法可能有很多種,其中利用地球磁場來進行導航的能力正是本篇論文的研究主題;利用地磁來導航的能力稱為磁感能力,目前有一個以量子力學為基礎的理論認為,地球磁場會間接影響鳥類體內某些分子的化學反應,進而影響鳥類的飛行方向,研究人員將這個化學磁感理論稱為自由基對機制(radical pair mechanism)。
    本篇論文將藉由量子力學所建立之自由基對系統的數學模型,來分析自由基對的特性,並藉由數值模擬來了解鳥類是如何利用地球磁場來指引其方向。接著我們提出利用人造自由基對分子C-P-F製作人造導航裝置的方法,並透過數值模擬分析其可行性。最後我們嘗試利用量子控制來控制自由基對分子的狀態,並且結合前述的人造導航裝置,我們分析實作出一個改良型磁感化學羅盤的可能性。

    Migration behavior is a seasonal regular activity of birds. Long-distance traveling with definite heading direction is the feature of this activity. From the observation of bird's behavior experiments, scientists discover that birds use plenty of methods to navigate. One of those navigation methods is using earth magnetic field that is the topic to be studied in this thesis. The ability of navigation using earth magnetic field is known as magnetoreception. Currently, a theory based on quantum mechanics reports that the magnetic field of Earth can indirectly affect some molecular chemical reactions of birds, and thereby change the direction of the flight of birds. The researchers called this chemical magnetoreception process radical pair mechanism.
    We plan to use quantum mechanics to build a model for radical pairs system, and to analyze its characteristics. In addition, by the assistance of numerical simulation we will reveal how birds can utilize earth magnetic field to guide their flying path. Moreover, we propose an navigation magnetoreception artificial eyeball build by the artificial synthetic radical pair molecule. Finally, we try to apply quantum control to control the quantum state of radical pairs, and combining the artificial eyeball we mentioned, we plan to use quantum control to improve the performance of magnetoreception chemical compass.

    摘要 i Abstract ii 致謝 viii 目錄 ix 表目錄 xiii 圖目錄 xiv 符號表 xviii 第一章 緒論 1 1.1 文獻回顧 1 1.2 研究動機與目的 4 1.3 章節架構 6 第二章 自由基對機制的原理與分析 8 2.1 自由基對磁感機制簡介 8 2.2 自由基對分子的磁場效應與反應流程 10 2.3 自由基對系統的數學描述 13 2.3.1 自由基對分子的Hamiltonian算符 13 2.3.2 單重態與三重態產量的數學表示式 17 2.3.3 單重態與三重態產量的數值計算 20 2.4 自由基對系統的模型建立與模擬 22 2.4.1 三粒子的自由基對系統 23 2.4.2 H算符的張量相乘矩陣表示法 25 2.4.3 四粒子自由基對系統 31 2.4.4 N粒子自由基對系統 33 2.5 自由基對系統磁敏感度之探討 35 第三章 鳥類磁感羅盤的模擬 45 3.1 鳥類磁感視覺圖形之分析 45 3.2 鳥類視覺圖形的模擬 49 3.3 鳥類飛行姿態與視覺羅盤的關係 51 3.4 鳥類飛行路徑與視覺羅盤的分析 54 3.5 不同飛行路徑下鳥類視覺羅盤的變化與討論 57 第四章 導航用磁感人工眼球的原理與分析 61 4.1 磁感人工眼球的構造及運作原理 61 4.2 磁感人工眼球的數值模擬 63 4.3 人造磁感裝置與鳥類磁感機制的比較 67 第五章 自由基對系統的量子控制 69 5.1 自由基對分子的狀態分析 69 5.2 量子系統的量子控制律推導 71 5.3 自由基對分子的狀態控制與模擬 74 第六章 自由基對狀態量子控制的應用 80 6.1 改良型人造磁感化學羅盤的系統組成與配置 80 6.2 改良型人造磁感化學羅盤之操作原理 81 6.3 單一磁受體系統的單重態比例控制 83 6.4 改良型人造磁感化學羅盤之模擬步驟與結果 84 6.5 自由基對系統的磁敏感度量子控制 86 第七章 總結 88 7.1 結果與討論 88 7.2 未來展望 90 參考文獻 93 附錄A 98 A.1 量子力學的數學基礎 98 A.1.1 量子力學中的向量 98 A.1.2 線性算符 98 A.1.3 算符的矩陣表示式 99 A.1.4 基本的線性算符 100 A.2 量子力學的四大公設 102 A.3 Hamiltonian算符 104 A.4 薛丁格方程式 105 A.5 期望值與密度算符 105 A.6 密度矩陣元素的物理意義 106 A.7 量子Liouville方程式 107 附錄B 109 電子自旋態 109

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