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研究生： 郭弈翔
Kuo, I-Hsiang
論文名稱： 2+1維度的宇宙膨脹偽熵
2+1 Dimensional Pseudo Entropy for Cosmological Expansion
指導教授： 朱創新
Chu, Chong-Sun
口試委員: 陳江梅
Chen, Chiang-Mei
張敬民
Cheung, Kingman
學位類別： 碩士
Master
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2023
畢業學年度： 111
語文別： 英文
論文頁數： 41
中文關鍵詞： 糾纏熵 、偽熵 、宇宙膨脹度規
外文關鍵詞： Entanglement entropy, Pseudo entropy, Cosmological expansion metirc
相關次數： 點閱：14  下載：0 
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    • 偽熵是一個取決於初始態和最終態，推廣糾纏熵的新量度。基於已知結果表
    明量子纏繞熵和偽熵均具有面積定律特性，我們對一個（2 + 1）維度的宇宙膨
    脹度規進行了測試，以確定面積定律的有效性以及時間因素對偽熵值的影響。
    此外，我們引入了量子猝滅的概念，以進一步探索可能存在的有趣現象。

    Pseudo entropy is a novel quantity that generalizes the concept of entanglement
    entropy, depending on both an initial state and a final state. Based on the wellknown
    results indicating that both entanglement entropy and pseudo entropy
    exhibit the area law property, we conducted tests on a (2+1)-dimensional cosmological
    expansion metric to determine the validity of the area law and how the time
    factor affects the value of pseudo entropy. Additionally, we analysis the concept
    of quantum quench to further explore any potential interesting phenomena.

    Contents Contents ii List of Figures iii 1 Introduction 1 2 Theoretical Background 3 2.1 Entropy and Area Law . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Entanglement Entropy for 2-Coupled Oscillators . . . . . . 5 2.1.2 Entanglement Entropy for N-Coupled Oscillators . . . . . . 6 2.1.3 Entanglement Entropy for Massless Field . . . . . . . . . .7 2.2 Correlator Method for Entanglement Entropy . . . . . . . . . 8 2.2.1 Correlation Function and Quantum State . . . . . . . . . . 9 2.2.2 Correlation Function and Coupling Matrix . . . . . . . . . 11 2.2.3 Fitted Curve for Entanglement Entropy . . . . . . . . . . .12 2.3 Pseudo Entropy for Free Field Theories . . . . . . . . . . . 14 2.3.1 Pseudo Entropy for 2-Coupled Oscillators . . . . . . . . . 15 2.3.2 Correlator Method for Pseudo Entropy . . . . . . . . . . . 17 2.3.3 Operator Method for Pseudo Entropy . . . . . . . . . . . . 20 2.4 Pseudo Entropy for (1+1) Scalar Field . . . . . . . . . . . .25 3 (2+1)D Pseudo Entropy 28 3.1 (2+1)D Pseudo entropy for cosmological expansion . . . . . . 28 3.1.1 Massive and Almost Massless Limit . . . . . . . . . . . . .32 4 Quantum Quenches 34 4.1 Global Quench for (2+1)D Pseudo Entropy . . . . . . . . . . .34 5 Conclusions and Discussions 38

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