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3522-50-7 | **檸檬酸鐵**，可視為三價鐵（Fe3+
）和檸檬酸所衍生的幾種共軛鹼。這些錯合物大多呈橙色或紅褐色固體，微溶於熱水，其水溶液在 pH 值小於 2 的環境下呈橘色或橘黃色，大於 2 時則變為綠色。
檸檬酸鐵在生物體中為代謝鐵的重要化合物。例如植物根部與一些微生物釋出檸檬酸根離子，以便從土壤中不溶性的含鐵化合物（如氫氧化鐵）中提取鐵，並形成可被有機體所吸收的檸檬酸鐵鹽。
檸檬酸鐵在醫學上用於透析血液並調節慢性腎臟病患者的鐵水平。它作用於飲食中存在的磷酸鹽並形成難溶性化合物，從而減少消化系統對其的吸收。
## 結構
由於檸檬酸鐵容易形成錯合物、低聚物和聚合物，因此，檸檬酸鐵不能明確的被單個定義，應視為同一族化合物，且其所有複合物都具有相同的分子式和不同的結構。
而這些複合物擴散到整個溶液，不同形式的檸檬酸鐵可以並存。在達到酸鹼平衡的狀態下，檸檬酸鐵會形成不溶性的紅色聚合物。其他環境條件下則為形成陰離子錯合物，如 [[Fe
2C
6H
4O
7]2(H
2O)2]2−。在過量檸檬酸根離子的情況下，鐵會形成帶負電的錯合物，例如 [Fe(C
6H
4O
7)2]5−和 [Fe
9O(C
6H
4O
7)8(H
2O)3]7−。
## 製備
檸檬酸鐵可以經由化學計量後將四水合硫酸鐵添加到 pH 值 3.0 的檸檬酸氫氧化鈉混合液中，再通過乙醇使此複合物沉澱。
## 化學性質
### 光還原
三價鐵離子在檸檬酸鐵（或三價鐵的羧酸鹽）通過光（特別是藍光和紫外光）還原後，會伴隨著與羥基相鄰的羧基氧化後以亞鐵離子狀態呈現，並產生二氧化碳和丙酮二羧酸鹽：
2Fe3++R2-C(OH)-CO−
2→2Fe2+
+ R2-C=O + H+
+ CO
2
其中 - R 表示 CH
2CO−
2 的官能基處。該反應無法在 pH 值 > 5.0 或 < 1.5 或者無水的非質子溶劑（如乙腈）環境下觀測。在 pH 值約 2.9 的水中，其可以達到最高量子效率，且即使在固態環境下也能反應。
該反應對於植物的新陳代謝亦有重要作用：土壤中的鐵質由根部吸收，而檸檬酸鐵溶解在樹汁裡，最終傳輸至葉片上照光還原為二價鐵，並轉運回植物細胞。
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] |
國立清華大學理學院 | **國立清華大學理學院**（英語：College of Science, National Tsing Hua University），隸屬於國立清華大學，為目前該校十二個學院之一。1956 年國立清華大學於台灣新竹市復校，成立原子科學研究所，下設數學組、物理組、放射化學組。而後先後成立數學系、物理系以及化學系，1973 年，經教育部核准，於清華各系所之上設立理、工、原子科學三個學院，沈君山為理學院首任院長。
## 沿革
* 1956 年：國立清華大學復校，成立原子科學研究所，下設數學組、物理組、放射化學組。
* 1958 年 5 月 25 日：舊物理館落成（現化工系館處）。
* 1963 年：成立數學研究所。
* 1964 年：成立數學系。
* 1965 年：成立物理學系。
* 1966 年：成立化學系及物理研究所（前原子科學所物理組）。同年 11 月，數學館落成。
* 1967 年：化學館落成。
* 1968 年：成立化學研究所。
* 1970 年：數學研究所增設應用數學組。
* 1971 年，清大天文台於舊物理館頂樓建成。
* 1972 年：應用數學組分出，單獨成立應用數學研究所，同時亦成立應用物理研究所、應用化學研究所。
* 1973 年：經教育部核准，將校內各系分設學院，成立**理學院**、工學院、原子科學院。
* 1974 年：成立分子生物研究所。
* 1977 年：成立計算機管理決策研究所。
* 1980 年：成立中國語文學系。
* 1982 年：成立外國語文學系。
* 1983 年：應用物理研究所併入物理研究所，應用化學研究所併入化學研究所。
* 1984 年：_中國語文學系_及_外國語文學系_轉隸人文社會學院。
* 1985 年：分子生物研究所更名為**生命科學研究所**
* 1988 年：物理系遷入落成之新物理館，舊館拆除；同年，計算機管理決策研究所更名為**資訊科學研究所**，應用數學所統計組另分出成立統計學研究所。
* 1989 年：綜合三館（又稱數學館）落成。
* 1990 年：成立資訊科學系。
* 1991 年：成立生物醫學研究所及生命科學系。同年，新天文台於新物理館頂樓重建。
* 1992 年：_生命科學系_、_生命科學研究所_及_生物醫學研究所_轉隸生命科學院。
* 1993 年：化學系館落成。
* 1995 年：物理研究所併入物理學系、化學研究所併入化學系，資訊科學研究所併入資訊科學系。 | [
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國立清華大學理學院 | * 1996 年：數學研究所及應用數學研究所併入數學系。
* 1998 年：_資訊科學系_轉隸電機資訊學院。
* 2001 年：天文研究所成立。
* 2003 年：物理學系增設光電物理組。
* 2006 年：成立理學院學士學位學程。
* 2008 年：成立清華基礎科學研究中心（校級中心，隸屬清華研發處），並與國家同步輻射研究中心合作，成立先進光源科技學位學程。
* 2010 年：理學院學士學位學程更名為**理學院學士班**。
* 2016 年：成立計算與建模科學研究所。
* 2017 年：物理學系增設天文物理組，為台灣第一個於大學部開設專攻天文物理領域之系組。
* 2022 年：先進光源科技學位學程停招，成立量子科技暨尖端材料博士學位學程。
## 系所單位
目前學院有三個學系、一個學士班學程、三個研究所，以及一個學位學程。
### 學系與學士班學程
* 數學系
* 物理學系
* 物理組
* 天文物理組
* 光電物理組
* 化學系
* 理學院學士班
### 研究所
* 天文研究所
* 統計學研究所
* 計算與建模科學研究所
### 學位學程
* 量子科技暨尖端材料學位學程
## 歷任院長
## 註解
## 參考資料
## 外部連結
* 國立清華大學理學院（頁面存檔備份，存於網際網路檔案館） | [
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結構形成 | **結構形成**，在物理宇宙學中是指星系、星系團和更大的結構在早期的微小密度波動中形成。從對宇宙微波背景輻射的觀測可知，宇宙大約在 138 億年前於一個炙熱、稠密、幾乎均勻的狀態中開始。然而，在今天的天空中，我們可以看到所有尺度的結構，從恆星和行星到星系，在更大尺度上的星系團和星系的片狀結構被包含少量星系的巨大空洞隔開。構造形成試圖模擬這些結構是如何由早期微小密度波紋的引力不穩定性形成。
現在的 Lambda-CDM 模型成功地預測了觀測到的星系、星系團和空洞的大尺度分布；但是在單個星系的尺度上，由於涉及重子物理、氣體加熱和冷卻、恆星形成和迴響的高度非線性過程，存在許多複雜狀況。無論是透過觀測，如哈伯超深空，還是通過大型電腦模擬，瞭解星系形成過程是現代宇宙學研究的一個主要課題。
## 概述
在現在的模型，可見宇宙的結構經由以下的階段形成：
### 極早期宇宙
在這一階段，一些機制，如宇宙膨脹，負責建立宇宙的初始條件：均勻性、各向同性、和平坦性。 宇宙膨脹也會將微小的量子波動（膨脹前）放大為密度過高和密度不足（膨脹後）的輕微密度波動。
### 結構生長
早期宇宙是由輻射控制的；在這種情況下，因為引力勢能波動保持不變，密度波動大於宇宙視界增長比例尺度因數。由於輻射控制阻礙了生長，小於視界的結構基本上仍然處於凍結狀態。 隨著宇宙膨脹，輻射密度下降得比物質快（由於光子能量的紅移）；這導致宇宙大爆炸後約 50,000 年出現了一種稱為物質 - 輻射相等的交叉現象。在這之後，所有的暗物質漣漪都可以自由生長，形成種子，重子隨後會落入其中。在這個時代的宇宙大小，在物質功率譜中形成一個轉換，可以用大的紅移量測來測量。
### 復合 | [
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結構形成 | 宇宙在這一階段的大部分時間裡都是由輻射控制的，由於強烈的熱量和輻射，原始的氫和氦完全被電離成原子核和自由電子。在這種熱且密集的情況下，在電子的湯姆森散射結束之前，輻射（光子）不能傳播得很遠。宇宙非常熱，密度很高，但膨脹得也很快，因此溫度持續下降而冷卻。最後，在大爆炸之後約 40 萬年，它變得足夠冷（大約 3,000K），質子可以捕獲帶負電的電子，形成中性的氫原子（由於氦原子有較大的結合能，在更早就形成）。一但幾乎所有的帶電粒子都被束縛在中性原子中，光子就不再與它們相互作用，在接下來的 138 億年中自由傳播；我們現在檢測到這些光子紅移了 1,090 倍，溫度降至 2.725K。它們成為宇宙微波背景（CMB，Cosmic Microwave Background），充塞在宇宙各處。幾次引人注目的太空任務 （COBE、WMAP、Planck），已經探測到 CMB 有非常微小的密度和溫度變化。雖然 CMB 在各個方向上幾乎是一致的，但這些變化是微妙的。然而，這十萬分之幾的微小溫度變化是非常重要的，因為它們基本上是早期的種子。宇宙中隨後所有的複雜結構與變化，最終都是從這些種子發展出來的。
在最初 40 萬年之後，宇宙發生的事情，層級結構的形成理論：較小的引力約束結構，像是包含第一顆恆星和星團的物質峰首先形成，以及隨後的氣體和暗物質合併形成星系，接著是星系群和星系團和星系的超星系團。
## 非常早期宇宙
## 相關條目
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] |
時間問題 | 理論物理學中，**時間問題**乃廣義相對論與量子力學間對於時間的概念衝突。量子力學中，時間的流動被視為絕對與同一的；廣義相對論中，時間的流動則是相對且受到環境的影響。此一問題涉及了物理學中，時間究竟為何？它是否是一真實存在、獨一的現象。另外時間似乎只有單方向的流動也是一個探討的主題，儘管目前不存在有一微觀的物理定律要求時間的單一流向。對巨觀系統來說，時間的流向則直接連結到一些第一原理，比如熱力學第二定律。
## 量子力學中的時間
在古典力學中，時間被賦予特殊角色，它被視為一個背景參數，在探討系統之外。在建構量子力學的標準過程中，如此的處理也被保留。實際上，這樣的處理方式與量子力學的主流哥本哈根詮釋交織在一起：所有對可觀測量的測量都是某個時刻進行的，而各種測量的結果有其一定的機率。
狹義相對論改變了對於時間的觀念。但對與某一選定參考系為靜止的觀察者而言，他或她的時間（「原時」概念）仍顯示為一個獨特、外在、全域的參數。牛頓力學觀點的時間在狹義相對論體系中呈現了一定程度的保留。
## 廣義相對論中絕對時間觀的顛覆
隨著廣義相對論的發表，時空不再是一絕對、靜態的實體，而是動態的；重力即是時空幾何形狀的表現。
物質與時空有所互動：
> 時空告訴物質如何運動；物質告訴時空如何扭曲。
>
>
此外，時空也可與自身發生交互作用，即重力波。時空的動態本質對於時間觀產生了廣大的影響。
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11079-26-8 | **雙環辛四烯合鈾**，化學式 U (C8H8)2，是一種有機鈾化合物，由一個鈾離子和兩個環辛四烯陰離子組成。它是最先被合成的有機錒系元素化合物之一。它是一種對空氣敏感，可溶於有機溶劑的綠色固體。雙環辛四烯合鈾，是雙環辛四烯合錒系元素的一員，由錒系元素和環辛四烯組成。它是研究最多的環辛四烯 - 金屬系統，儘管雙環辛四烯合鈾沒有實際用途。
## 製備、結構和成鍵
雙環辛四烯合鈾是由 Andrew Streitwieser 的團隊於 1968 年描述的。 他們的製備方法是在 0°C 下的 THF 里，環辛四烯二鉀和四氯化鈾反應而成：
:
雙環辛四烯合鈾對氧氣的活性很高，使得它可在空氣中自燃，但它對水解穩定。 它的分子結構是 U4+(C8H82−)2，其中的 η8- 環辛四烯陰離子是平面型的，包含 10 個 π- 電子，並且彼此平行，形成含有鈾原子的夾心型配合物。 固態時，雙環辛四烯合鈾中的兩個環辛四烯是重疊的，對稱性為 _D8h_ 。 在溶液中，環以低能壘旋轉。
電子光譜顯示鈾 - 環辛四烯基的化學鍵主要是由於鈾原子的 6d 軌道混入環辛四烯配體中的 π 分子軌道而成，因此將電子電荷捐贈給鈾，其中涉及鈾的 5f2 軌道的相互作用較小。 電子理論計算與該結果一致並指出，開殼的 5f 軌道與配體軌道的較弱相互作用決定了 | MJ|，即沿基態 8 倍對稱軸的角動量量子數的大小。
## 相關化合物
其它有 M (C8H8)2 結構的化合物有 M = （Nd、Tb、Pu, Pa、Np、Th 和 Yb）。雙環辛四烯合鈾的衍生物包括對空氣穩定的 U (C8H4Ph4)2 和環庚三烯類似物 [U (C7H7)2]−。 此外，化學式類似的雙環辛四烯合鐵有非常不同的結構，其中含有 η6- 和 η4- 的 C8H8 配體。
## 參考資料
## 擴展閱讀
* _The f elements_, Nikolas Kaltsoyannis and Peter Scott. ISBN 0-19-850467-5
* _Chemistry of the Elements_, N. N. Greenwood and A. Earnshaw. ISBN 0-08-022057-6
* Lanthanides & Actinides: Organoactinides （頁面存檔備份，存於網際網路檔案館） | [
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效率 | **效率**（Efficiency）是指在適當的使用原料、能源、努力、金錢及時間的情形下，進行特定事務或產出預期成果的能力。以廣義的定義來說，效率是可以成功的把事情作好，且沒有浪費的能力。「效率本身不是目的，效率不是我們想要的，但效率可以讓我們獲得更多有價值的事物。」。在較數學或科學的用語中，效率是量測輸入用在預期任務或輸出的程度。一般會包括以最小的浪費、支出以及努力的情形下，用特定的努力來產出特定成果的能力。在不同的產業領域中，效率會指不同的輸入及輸出。
效率（Efficiency）很容易和有效果（effectiveness）混淆。大致來說，效率是可以量測的概念，可以用可用輸出除以總輸入的比例來表示。有效果是表示是否可以完成特定的成果，也可以用量化方式表示，但只需要用到加法即可。效率可以先考慮理想結果，再以理想結果的百分比來表示，例如在沒有摩擦力或其他能量損失的情形下，燃料中的能量會完全轉換為想要的功。有時也會將效率表示為非百分比的數值，例如比沖。
簡單來說，可以用二句話來區分效率和有效性「效率是以正確的方式做事，有效果是把事情做完。」。以工廠生產來說，若工人願意花更長時間工作，或是被迫長時間工作，工人可以用沒有效率的製程，完成眾多產品的生產。同樣的，工廠也可以用耗費更多能源或人力的方式生產大量的產品，雖然有效果，但沒有效率，但若能源或人力成本較競爭廠商低廉，工廠有可能會這麼做。
效率常常會表示為可用輸出和總輸入的比，用數學公式可以表示為 _r_=_P_/_C_，其中的 _P_ 是可用的輸出（產出），而 _C_ 是總成本或是總輸入。這可以用在產出以及消耗品都以可以用可比較的單位量化的情形，而且消耗品是以守恆的過程轉換為產出。例如在熱力學中分析熱機的能量轉換效率時，_P_ 是可以輸出的功，而 _C_ 是高溫端熱輸入的量。由於能量守恆定律，_P_ 一定不會大於 _C_，因此效率 _r_ 不可能超過 100%（因為熱力學第二定律，效率的上限值會更低）。
## 科學及技術領域
### 物理
* 可用功輸出相對能量輸入的比例，一般會用希臘字母 η 表示；
* 電效率
* 能量轉換效率
* 機械效率
* 熱效率，產出的功相對消耗熱能的比例
* 能源效率
* 熱力學：
* 能量轉換效率，量測熱力學第二定律的損失
* 輻射效率：天線端子輻射能量相對吸收能量的比例
* 容積效率，針對 RAF 設計的內燃機
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] |
效率 | * 法拉第效率，電解
* 量子效率，量測光感元件的靈敏度
* 光柵效率，廣義的鏡子反射率，延伸到繞射光柵。
### 經濟
* 經濟效率，避免浪費或避免不想要特質的程度
* 效率市場假說，符合理想市場的程度
* 帕累托最優，在各方面的取捨已有最佳應用，若某一項再提昇，其他項目可能就會退步的情形
* 卡爾多改進，弱化版的帕累托最優
* 分配效率，貨物的理想分配
* 效率工資，因為生產力較好，付給員工高於市場的薪資
* 企業效率，盈餘相對於支出的比例
* 進步時代（1890-1932）的效率運動，提倡經濟、社會及政府的效率
* CP 值，性能和價格的比例。
### 其他科學領域
* 計算：
* 演算法效率，電腦程式速度以及記憶體需求的最佳化
* 儲存效率，電腦資料儲存的有效性
* 效率因子，資料傳輸通訊用語
* 效率 (統計學)，估測量理想程度的量測
* 材料效率，比較建築計劃或實體過程的材料需求
* 行政效率，評估行政機關的透明度，以及針對市民及企業的流程或程序簡化
* 光合效率
## 相關條目
* 不效率
* Jevons 悖論
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吸收式制冷 | **吸收式製冷**（absorption refrigerator）是利用熱源作為製冷能量來源的製冷系統，熱源可以是太陽熱能、燃燒化石燃料、工廠廢熱、或來自區域供暖系統。系統中有兩種冷媒，一種會蒸發冷卻，由第二種冷媒吸收。之後會再加熱，讓這兩種冷媒恢復到原始狀態。此一原理也可以用在空氣調節的大樓中，用燃氣渦輪引擎的廢熱或是熱水器的熱。若利用燃氣渦輪引擎的廢熱，在能源效率上的效率很高，因為先產生電、接著產生熱水，最後可以有冷氣的熱電聯產。吸收式製冷常用在休旅車、露營車以及拖掛式房車上，因為可以用丙烷作為能量來源，不需要電力。吸收式製冷和蒸氣壓縮製冷不同，除了讓冷媒流動之外，不需要其他的可動件。
## 原理
常見的吸收式製冷裝罝類似蒸氣壓縮製冷裝置，也會用沸點很低（低於 - 18°C）的冷媒。壓縮製冷的冷媒常會選氫氯氟烴（HCFC）或氫氟烴（HFC），而吸收式製冷裝罝會用氨或是水為冷媒，而且會有第二種冷媒（吸收劑，absorbent）可以吸收前述冷媒的氣體。冷媒可能是水（冷媒是氨的情形）或是鹽水（冷媒是水的情形）。兩種都是用蒸發冷卻的原理：當冷媒蒸發（或沸騰），會帶走熱量，因此會有冷卻的效果。二個的差異是冷媒由氣態變成液態（因此可以重覆冷卻循環）的方式，吸收式製冷裝罝的冷媒單純只用熱量傳輸使其由氣態變成液態，除了讓冷媒流動外，不需要其他的可動件。
吸收式製冷循環可以分為以下三段：
1. 蒸發：液態冷媒在低分壓環境下蒸發，從環境中（例如冷藏室）吸熱。因為分壓較低，使其蒸發需要的溫度比較低。
2. 吸收：第二種液態冷媒（在耗盡狀態下），會吸收氣態的冷媒，維持較低的分壓。會產生氣態冷媒飽和的液體，進入下一階段。
3. 再生：將冷媒飽和的液體加熱，使其中的氣態冷媒蒸發。
: : a. 蒸發是在細管的下端，氣態冷媒的泡泡將冷媒耗盡的液態推到較高的腔室，之後會因為重力使其流到吸收腔。
: b. 熱的氣態冷媒流過熱交換器，將熱傳送到系統以外（例如冰箱外的室溫空氣），在較高處凝結。凝結後的液態冷媒會因重力流動，以提供蒸發階段需要的冷媒。
因此系統有沒有泵浦的情形下，會提供力學式的循環。
在凝結時，為了避免一些壓力上的問題，會加入第三種氣態。 | [
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吸收式制冷 | 和壓縮製冷比較，壓縮製冷會使用壓縮機，可能是電力或是內燃機驅動，以增加氣態冷媒的壓力。所得的高溫、高壓氣體會在暴露在外在環境下（多半是室內的空氣）的熱交換器（冷凝器）中凝結為液體。凝結的液體溫度接近室溫，但壓力較高，會通過節流孔或節流閥進入蒸發區。節流孔或節流閥會在高壓凝結區以及低壓蒸發區之間產生壓力差。蒸發區的低壓會使液態冷媒蒸發，同時吸收冷藏室內的熱。氣態冷媒會回到壓縮機，重覆此一循環。
### 簡易的鹽水系統
大型商業場所中用的簡易吸收式製冷系統會用溴化鋰或氯化鋰鹽以及水。水在低壓下會在要冷卻的盤管內蒸發。水會吸收到溴化鋰（或氯化鋰）鹽水溶液中。系統再透過熱，將水從溴化鋰鹽水中蒸發出來。
### 噴水吸收製冷系統
另一種製冷會使用空氣、水以及鹽水溶液。吸入的溫暖潮濕空氣會通過噴灑鹽水的腔室中，會使空氣降低濕度，但不會降低溫度，之後再讓空氣通過蒸發冷卻器，其中會噴灑淡水，使空氣降溫，並增加濕度。低溫的空氣會再通過另一個通過噴灑鹽水的腔室中，去除濕度，得到乾冷的空氣。
鹽水溶液會在低壓下加熱，使水蒸發。蒸發的水蒸氣會再凝結成液態的水，接到蒸發冷卻器中。
### 單壓吸收製冷系統
單壓吸收冷卻系統的原理是依液體的蒸發速度是依其蒸氣的分壓而定，若分壓較低，會蒸發的比較快。在維持系統總壓相等的前提下，冷卻系統在低溫的冷卻部份，讓冷媒維持在分壓較低的條件下（以提高蒸發速率），在和外部空氣接觸，散熱到外界時，讓冷媒維持在分壓較高的條件下（降低蒸發速率）。
冷卻系統中有三種物質：氨、氫氣和水。循環是封閉的，因此所有的氨、氫氣和水都可以重覆使用。此系統會加壓，使氨的沸點超過冷凝管（冷卻系統傳熱到外部，溫度會比空氣高）的溫度，此壓力一般會是 14–16 atm，此壓力下氨的露點為 35 °C。
冷凍循環的開始，室溫下的液氨會進入蒸發器中。蒸發器的容積較液氨的體積較大，多出來的空間是由氫氣及氨氣所填充。氫氣的存在會降低氨氣的氣體分壓，因此使液氨的蒸發溫度低於蒸發器內的溫度。氨氣蒸發，並且從液氨中帶走一部份的熱，使液氨溫度降低。冷卻系統較熱的部份會有熱流到較冷的液體，讓液氨進一步的蒸發。
在接下來的二個步驟中，會將氨氣和氫氣分離，因此可以重新使用氨氣。 | [
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] |
吸收式制冷 | 1. 氨氣和氫氣的混合氣體會經由管路，從蒸發器流到吸收器中。在吸收器中，混合氣體會和水溶液接觸，氨氣會溶在水溶液中，氫氣不會，因此吸收器的上方會是氫氣，吸收器的下方則是高濃度的氨水溶液，此程序可以分離氫氣（不溶於水）和氨氣（溶在水中）。
2. 下個步驟會分離氨氣和水。氨水溶液會流到產生器（鍋爐）中，會加熱讓氨氣沸騰汽化，留下沸點較高的水。有些水蒸氣和泡沫會和氨混合，最後一個步驟會將氨氣（和少許水蒸氣）流到分離器，是往上彎曲的管道，有小的障礙物以消除泡沫，並且讓水在管壁凝結流回產生器中。
純氨氣會再流到凝結器內。熱的氨氣在換熱器中會和空氣進行熱交換，空氣溫度比高壓的氨沸點要低，因此氨氣會凝結成液氨。凝結後的液氨會往下流，和吸收器釋放的氫氣混合，重覆此一循環。
## 相關條目
* 吸附式製冷
* Icyball
* 量子吸收式製冷
* 露營車
## 參考資料
## 延伸閱讀
* Levy, A.; Kosloff, R. Quantum Absorption Refrigerator. Phys. Rev. Lett. 2012, **108**: 070604. Bibcode:2012PhRvL.108g0604L. PMID 22401189. arXiv:1109.0728 . doi:10.1103/PhysRevLett.108.070604.
## 外部連結
* Absorption Heat Pumps（頁面存檔備份，存於網際網路檔案館） (Office of Energy Efficiency and Renewable Energy).
* Arizona Energy（頁面存檔備份，存於網際網路檔案館） Explanation with diagrams
* Lithium-Bromide / Water Cycle（頁面存檔備份，存於網際網路檔案館） – Absorption Refrigeration for Campus Cooling at BYU.
* American National Standards Institute. AHRI standard 560–2000 for absorption refrigerators (PDF). [2012-03-31]. （原始內容存檔 (PDF) 於 2012-10-31）. | [
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] |
約翰·普雷斯基爾 | **約翰・菲利普・普雷斯基爾**（英語：John Phillip Preskill，1953 年 1 月 19 日 —）是一位美國理論物理學家，也是加州理工學院理察・費曼理論物理學教授，也是該校量子信息與物質研究所所長。
普雷斯基爾是量子資訊科學和量子計算領域居領導地位的一位科學家，以創造量子計算優越性一詞而聞名。
## 參考資料
## 外部連結
* 維基共享資源上的相關多媒體資源：約翰・普雷斯基爾
* Preskill's Caltech homepage （頁面存檔備份，存於網際網路檔案館）
* Institute for Quantum Information at Caltech | [
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光學環形諧振器 | **光學環形諧振器**由至少一個光路封閉的波導以及光線的輸入與輸出端 (比如波導) 所組成。光學環形諧振器的概念與迴音廊相仿，不同處在於使用光線，並且需遵守建設性干涉與全內反射條件。當符合共振條件的光線從輸入端波導進入，並經過環形波導，在環形波導裡由於建設性干涉而逐漸增加光強，最後在輸出端波導輸出。
由於只有特定的波長的光才能在環形波導中發生共振，整個光學環形諧振器可視為是一個濾波器。此外，兩個或多個環形波導可以互相耦合，產生出加 / 減光學濾波器。
## 背景
光學環形諧振器的原理包含：全內反射、建設性干涉與光學耦合。
### 全內反射
由於全內反射，光線在光學環形諧振器裡傳播時會留在波導內。當光線打到傳播介質的邊界時，若入射角大於臨界角，且邊界另一側物質的折射率較低，全內反射便會發生，不會有光線通過邊界。為了讓光學環形諧振器良好運作，滿足全反射條件是必要的，應盡可能避免光線離開波導。
### 干涉
干涉是指兩個或多個波疊加成一個振幅更高或更低的合成波。而在建設性干涉時，兩個相同相位的波會相互干涉出一個振幅為兩波相加的合成波。當光線在繞行環形波導時，它會與其他待在環裡的光線互相干涉。因此，假設系統中沒有吸收、漸逝波、不完美耦合等因素造成的損失，且系統符合共振條件，則光學諧震器輸出的光強將會輸入的光強相同。
### 光學耦合
右圖中，由於漸逝波的效應，當光線從上方的波導經過時，部分的光線會耦合進入環形波導。有三個因素會影響耦合：波導之間的距離、波導之間能耦合的長度、折射率。減少波導間的距離、增加波導之間能耦合的長度都可以增加耦合效率。波導本身的折射率與波導與波導之間物質的折射率也會影響耦合效率。
一個關於耦合特性是臨界耦合 (critical coupling)，臨界耦合發生時，經過耦合區後不會有光強存在，所有的光線都會儲存在環型波導裡，並且在環裡耗散。(如頁首圖片所示範)
要讓臨界耦合發生，需要滿足以下公式:
: $|\mathrm {K} |^{2}+|t|^{2}=\mathbf {1} $
其中 t 是經過耦合區的透射係數， $\mathrm {K} $ 是耦合係數。
## 理論
要了解光學環形諧振器，要先理解環形諧振器的光程差 (OPD)。對於單環的環型諧振器有下式:
: $\mathbf {OPD} =2\pi rn_{eff}$ | [
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] |
光學環形諧振器 | 其中 r 是環狀波導的半徑， _$n_{eff}$_ 是波導材質的等效折射率，為了滿足全內反射條件， $n_{eff}$ 必須大於周圍物質的折射率，比如空氣。
為了讓共振發生，需要滿足共振條件:
: $\mathbf {OPD} =m\lambda _{m}$
_$\lambda _{m}$_ 是共振波長，m 代表諧振器的第幾個模態，為正整數。這個公式表明為了讓光線在環裡產生建設性干涉，環的圓周長必須是波長的整數倍。這個特性表示當含有多個波長的光線 (如白光) 進入諧振器時，只有共振波長的光線可以通過諧振器。
環形諧振器的品質因子 (Q 因子) 與細緻度 (finesse) 可以用以下公式定量描述 (參見參考資料: eq: 2.37,or eq:19+20):
: $\mathbf {Q} ={\frac {\lambda }{\delta \nu }}$
: ${\mathcal {F}}={\frac {\nu _{f}}{\delta \nu }}$
_${\mathcal {F}}$_ 是諧振器的細緻度， $\lambda $ 是光的波長， $\nu _{f}$ 是輸出光的自由光譜區 (FSR, free spectral range)， $\delta \nu $ 是輸出光的半峰全寬 (FWHM)。
品質因子可以用來決定任意環形諧振器的共振波長範圍，也可以用來量化諧振器在工作時的能量耗損，較低的 Q 因子通常代表較高的損耗。
## 雙環諧振器
雙環諧震器使用兩個環狀波導，它們可以串聯 (如右圖所示) 或並聯。串聯時，雙環諧振器的輸出方向與輸入相同。當輸入光符合第一個環的共振條件時，光線耦合進入第一個環，並沿著環傳播。若光線符合第二個環的共振條件，光線會從第一個環耦合到第二個環。依同樣方式，光線最終會耦合到輸出波導。
要讓目標光線能通過雙環諧震器，需要符合下條件:
: $\ 2\pi n_{1}R_{1}=m_{1}\lambda _{1}$
: $\ 2\pi n_{2}R_{2}=m_{2}\lambda _{2}$
$m_{1}$ 與 $m_{2}$ 是第一與第二個環的模態數 (mode number)，為正整數。要讓同樣波長的光線穿過整個系統，所以 $\lambda _{1}=\lambda _{2}$ 。
整理後得到: | [
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光學環形諧振器 | : $\ {\frac {n_{1}R_{1}}{m_{1}}}={\frac {n_{2}R_{2}}{m_{2}}}$
其中 $m_{1}$ 與 $m_{2}$ 為整數。
雙環諧振器可做為可調變的反射濾波器 (如右圖)。
## 應用
由於光學諧振器能過濾特定波長的光線，可以透過使用多個光學諧振器製造出高階數的光學濾波器。光學諧振器有 "小尺寸、低損耗、可整合進現存光學系統" 的優點。除此之外，由於可以透過改變環的半徑來改變共振波長，整個諧振器可以視為可調變的系統，這個特性可以用來製作某些力學感應器。若諧振器受到應力作用，發生尺寸變化，則光線的共振波長也會跟著改變。這個效果可以用來監測光纖或波導是否發尺寸變化。
除了改變半徑，也可以改變折射率進行調變，比如透過熱、電磁、全光 (all-optical) 效應。電磁與全光效應比起熱與力學反應的更快，適合應用在光通訊裡。
環形、圓柱形和球形的光學諧振器可應用在生物傳感的領域中。 如何增加生物傳感器的性能是其中一個研究重點。 使用光學諧振器作為生物傳感器的優點是只需少量的樣品就能測得光譜，並且能大大的減少溶劑和雜質造成的拉曼和螢光訊號。諧振器也被用於氣體的化學鑑定，用來測量吸收光譜。
一些科學家關注於製作高 Q 因子的三維的球形諧振器，這些介電球 "被提議作為低損耗的光學諧振器，用來進行雷射冷卻以研究腔量子電動力學，或者用來檢測單個捕獲原子的超敏感檢測器。"
環形諧振器也可以在量子資訊實驗中作為單光子源。 許多用於製作光學諧振器的材料在高光強下會有非線性效應出現，這些非線性允許四波混頻與自發參量下轉換等頻率調變過程出現，後者可用來生成光量子對。
## 參見
* 全內反射
* 耦合 \_(物理學)
* 濾光器
* 光開關
## 參考資料
* YouTube 上的光學環形諧振器的模擬動畫 （頁面存檔備份，存於網際網路檔案館）
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林德布拉德方程 | 量子力學中，**林德布拉德方程**（英語：Lindblad equation）是最常用的主方程之一，其常用來描述密度矩陣的含時演化（通常是非么正的）。
薛丁格方程是林德布拉德方程在特殊情況的推論。薛丁格方程展現的是系統的態矢量隨時間的演化，只能處理純態演化，而林德布拉德方程所展現的是系統的密度矩陣隨時間的演化（密度矩陣可以表徵系統的混態），所以林德布拉德方程比薛丁格方程更加一般。
## 由來
在量子力學系統的演化中，如果系統所有的自由度都能被充分考慮，就可以認為系統的含時演化是么正的，也就是說不存在衰減（decay）和退相干等現象。但是，任何真正的物理系統都不是絕對孤立的，其必定會與環境有一定的作用，從而導致衰減和退相干等現象，這也是量子效應難以在宏觀尺度上進行觀察的原因。
現已有許多數學方法來描述與環境進行相互作用的量子力學系統的含時演化，其中一種便是使用密度矩陣及其對應的主方程。原則上來說，這種方法與薛丁格繪景以及海森堡繪景是等價的，但是其能更容易地處理與環境作用而導致的各種現象。密度矩陣則可以很好地描述混態，這對於準確描述開放量子力學系統（英語：open quantum system）是至關重要的。
## 定義
一般來說， $N$ 維系統密度矩陣的林德布拉德方程可寫為：
$$
{\frac {{\text{d}}\rho }{{\text{d}}t}}=-{\frac {i}{\hbar }}[H,\rho ]+\sum _{n,m=1}^{N^{2}-1}h_{nm}(A_{n}\rho A_{m}^{\dagger }-{\frac {1}{2}}\{A_{m}^{\dagger }A_{n},\rho \})
$$
其中 $H$ 表示系統的哈密頓量（厄米的）； $\{A_{m}\}$ 是希爾伯特空間中希爾伯特 - 施密特算子的任意一組正交基，滿足 $A_{N^{2}}$ 正比於單位矩陣；係數矩陣 $h$ 與哈密頓量 $H$ 一同決定了系統的演化，其中 $h$ 必須是半正定的。反對易式 $\{\cdot ,\cdot \}$ 定義為： $\{A,B\}=AB+BA$ 。
如果 $h_{nm}$ 均為 0，則林德布拉德方程就退化為封閉系統的劉維爾方程，即：
$$
{\frac {{\text{d}}\rho }{{\text{d}}t}}=-{\frac {i}{\hbar }}[H,\rho ]
$$ | [
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林德布拉德方程 | 該方程有時也被稱作馮諾伊曼方程，或劉維爾 - 馮諾伊曼方程（英語：Liouville-von Neumann equation）。
由於矩陣 $h$ 是半正定的，其可被一酉算符 $u$ 對角化：
$$
u^{\dagger }hu={\begin{bmatrix}\gamma _{1}&0&\cdots &0\\0&\gamma _{2}&\cdots &0\\\vdots &\vdots &\ddots &\vdots \\0&0&\cdots &\gamma _{N^{2}-1}\end{bmatrix}}
$$
其本徵值 $\gamma _{i}$ 是非負的。定義另一組正交基：
$$
L_{i}=\sum _{j=1}^{N^{2}-1}u_{ji}A_{j}
$$
就可將一般形式的林德布拉德方程改寫成對角化形式：
$$
{\frac {{\text{d}}\rho }{{\text{d}}t}}=-{\frac {i}{\hbar }}[H,\rho ]+\sum _{i=1}^{N^{2}-1}\gamma _{i}(L_{i}\rho L_{i}^{\dagger }-{\frac {1}{2}}\{L_{i}^{\dagger }L_{i},\rho \})
$$
$L_{i}$ 一般稱作系統的林德布拉德算符（英語：lindblad operator）或躍遷算符（英語：jump operator）。
## 推導
對於開放量子系統，不僅要關注系統本身（ $S$ ），還應考慮所處環境 ( $B$ ) 對系統的影響。從而整體希爾伯特空間 ${\mathcal {H}}$ 應為系統 ${\mathcal {H}}_{S}$ 與環境 ${\mathcal {H}}_{B}$ 希爾伯特空間的張量積，即： ${\mathcal {H}}_{S}={\mathcal {H}}_{S}\otimes {\mathcal {H}}_{B}$ 。因此總系統的哈密頓量可寫為：
$$
H=H_{S}\otimes I_{B}+I_{S}\otimes H_{B}+H_{I}
$$
其中 $H_{S}$ ， $H_{B}$ 和 $H_{I}$ 分別表示系統、環境以及系統與環境相互作用的哈密頓量。 $I$ 是單位矩陣。 | [
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林德布拉德方程 | 設初始時刻整體系統（量子系統與環境）的密度算符為 $\rho (0)=\rho _{S}(0)\otimes \rho _{B}$ 。這裡 $\rho _{S}(0)$ 表示量子系統的初態， $\rho _{B}$ 為環境的密度矩陣，假設其不隨時間變化。此時總系統的動力學演化仍是么正的，於是在相互作用表象下，劉維爾方程可寫為（以下 $\hbar $ 均取 1）：
$$
{\frac {\text{d}}{{\text{d}}t}}\rho (t)=-i[H_{I}(t),\rho (t)]
$$
其積分形式為：
$$
\rho (t)=\rho (0)-i\int _{0}^{t}{\text{d}}\tau [H_{I}(\tau ),\rho (\tau )]
$$
將積分形式帶入原式中：
$$
{\frac {\text{d}}{{\text{d}}t}}\rho (t)=-i[H_{I}(t),\rho (0)]-[H_{I}(t),\int _{0}^{t}{\text{d}}\tau [H_{I}(\tau ),\rho (\tau )]]
$$
將上式兩邊同時對環境部分自由度求偏跡，假設量子系統與環境的耦合較弱，便可採用玻恩近似： ${\text{tr}}_{B}[H_{I}(t),\rho (0)]=0$ ，可得：
$$
{\frac {\text{d}}{{\text{d}}t}}\rho _{S}(t)=-\int _{0}^{t}{\text{d}}\tau {\text{tr}}_{B}[H_{I}(t),[H_{I}(\tau ),\rho (\tau )]]
$$
根據量子系統與環境的耦合較弱的假設，可以認為： $\rho (t)\approx \rho _{S}(t)\otimes \rho _{B}$ ，帶入上式得到：
$$
{\frac {\text{d}}{{\text{d}}t}}\rho _{S}(t)=-\int _{0}^{t}{\text{d}}\tau {\text{tr}}_{B}[H_{I}(t),[H_{I}(\tau ),\rho _{S}(\tau )\otimes \rho _{B}]]
$$ | [
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] |
林德布拉德方程 | 為進一步簡化上述方程，採用馬爾可夫近似（英語：Markov approximation），即 $t$ 時刻系統狀態僅與當前時刻有關，從而可將被積函數 $\rho _{S}{\tau }$ 替換為 $\rho _{S}{t}$ ，同時將 $\tau $ 變換為 $t-\tau $ ，並把積分上限拓展到無窮（當環境的弛豫時間尺度遠大於所研究的時間範圍尺度時，上述操作是合理的），最終得到玻恩 - 馬爾科夫主方程：
$$
{\frac {\text{d}}{{\text{d}}t}}\rho _{S}(t)=-\int _{0}^{\infty }{\text{d}}\tau {\text{tr}}_{B}[H_{I}(t),[H_{I}(t-\tau ),\rho _{S}(t)\otimes \rho _{B}]]
$$
在薛丁格表象下，系統與環境相互作用哈密頓量可寫為：
$$
H_{I}=\sum _{\alpha }A_{\alpha }\otimes B_{\alpha }
$$
其中 $A_{\alpha }$ 表示系統算符， $B_{\alpha }$ 表示環境算符，定義系統的躍遷算符：
$$
A_{\alpha }(\omega )=\sum _{\xi '-\xi =\omega }\Pi (\xi )A_{\alpha }\Pi (\xi ')
$$
這裡 $\xi $ 是系統的本徵能量。於是在相互作用表象下，系統與環境相互作用的哈密頓量可寫為：
$$
H_{I}(t)=\sum _{\beta ,\omega }e^{-i\omega t}A_{\beta }(\omega )\otimes B_{\beta }(t)=\sum _{\alpha ,\omega '}e^{i\omega 't}A_{\alpha }^{\dagger }(\omega ')\otimes B_{\alpha }^{\dagger }(t)
$$
將其帶入玻恩 - 馬爾科夫主方程中，忽略掉快速震盪項，並定義 $\Gamma _{\alpha \beta }(\omega )$ ：
$$ | [
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林德布拉德方程 | \Gamma _{\alpha \beta }(\omega )=\int _{0}^{\infty }{\text{d}}\tau e^{i\omega \tau }\langle B_{\alpha }^{\dagger }(t)B_{\beta }(t-\tau )\rangle
$$
基於玻恩近似，假設環境處於穩態，則 $[H_{B},\rho _{B}]=0$ ，那麼 $\langle B_{\alpha }^{\dagger }(t)B_{\beta }(t-\tau )\rangle =\langle B_{\alpha }^{\dagger }(\tau )B_{\beta }(0)$ ，這表明 $\Gamma _{\alpha \beta }(\omega )$ 不依賴於時間。
最後得到相互作用表象下的林德布拉德方程：
$$
{\frac {\text{d}}{{\text{d}}t}}\rho _{S}(t)=-i[H_{LS},\rho _{S}(t)]+{\mathcal {D}}(\rho _{S}(t))
$$
其中 ${\mathcal {D}}(\rho _{S}(t))$ 可表示為：
$$
{\mathcal {D}}(\rho _{S}(t))=\sum _{\alpha \beta }\sum _{\omega }\gamma _{\alpha \beta }(\omega )\left(A_{\beta }(\omega )\rho _{S}(t)A_{\alpha }^{\dagger }(\omega )-{\frac {1}{2}}{A_{\alpha }^{\dagger }(\omega )A_{\beta }(\omega ),\rho _{S}(t)}\right)
$$
$H_{LS}$ 、 $S_{\alpha \beta }(\omega )$ 、 $\gamma _{\alpha \beta }(\omega )$ 分別為：
$$
H_{LS}=\sum _{\alpha \beta }\sum _{\omega }S_{\alpha \beta }(\omega )A_{\alpha }^{\dagger }(\omega )A_{\beta }(\omega )
$$
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] |
林德布拉德方程 | S_{\alpha \beta }(\omega )={\frac {1}{2i}}(\Gamma _{\alpha \beta }(\omega )-\Gamma _{\beta \alpha }^{*}(\omega ))
$$
$$
\gamma _{\alpha \beta }(\omega )=\Gamma _{\alpha \beta }(\omega )+\Gamma _{\beta \alpha }^{*}(\omega )
$$
## 例子
對於一個二能級系統，取其基態記為 $|0\rangle $ ，激發態記為 $|1\rangle $ 。則系統的哈密頓量 $$ 為： $H=J(\sigma _{x}+G\sigma _{z})$ 。 $\sigma _{x}$ 、 $\sigma _{z}$ 為泡利矩陣。該體系的林德布拉德方程為：
$$
{\dot {\rho }}=-i[H,\rho ]+\sum _{k}l_{k}\rho l_{k}^{\dagger }-{\frac {1}{2}}(l_{k}^{\dagger }l_{k}\rho +\rho l_{k}^{\dagger }l_{k})
$$
考慮體系激發態的能量耗散，則上式中的 $l_{k}$ 應取 ${\sqrt {\Gamma }}\sigma ^{-}$ ，則對應的林德布拉德方程為：
$$
{\dot {\rho }}=-i[H,\rho ]+\Gamma \left[\sigma ^{-}\rho \sigma ^{+}-{\frac {1}{2}}(\sigma ^{+}\sigma ^{-}\rho +\rho \sigma ^{+}\sigma ^{-})\right]
$$
其中 $\sigma ^{+}=|1\rangle \langle 0|$ ， $\sigma ^{-}=|0\rangle \langle 1|$ ， $\Gamma $ 是與耗散速率有關的常數。
通過解上述方程即可得到體系存在能量耗散時的動力學演化過程。
## 參見
* 主方程
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] |
林德布拉德方程 | * Manzano, Daniel (2020). "A short introduction to the Lindblad master equation". AIP Advances. 10 (2): 025106. arXiv:1906.04478 （頁面存檔備份，存於網際網路檔案館）
* M. A. Nielsen, and I. L. Chuang, Quantum Computation, and Quantum Information[M], Cambridge, Cambridge University Press, 2010.
* 皇甫鏞.(2018). 主方程方法在開放量子系統動力學中的若干應用.
## 外部連結
* Quantum Optics Toolbox （頁面存檔備份，存於網際網路檔案館） for Matlab
* Master equation solver （頁面存檔備份，存於網際網路檔案館） from QuTiP （頁面存檔備份，存於網際網路檔案館）
* QuantumOptics.jl （頁面存檔備份，存於網際網路檔案館） the quantum optics toolbox in Julia.
* The Lindblad master equation | [
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后量子密码学 | **後量子密碼學**（英語：Post-quantum cryptography，縮寫：PQC），又稱**抗量子計算密碼學**，是密碼學的一個研究領域，專門研究能夠抵抗量子電腦的加密演算法，特別是公鑰加密（非對稱加密）演算法。不同於量子密碼學，後量子密碼學使用現有的電腦，不依靠量子力學，它依靠的是密碼學家認為無法被量子電腦有效解決的計算難題。
時至 2021 年，電腦與網際網路領域廣泛使用的公鑰加密演算法均基於三個計算難題：整數分解問題、離散對數問題或橢圓曲線離散對數問題，如 DH、ECDH、RSA、ECDSA。然而，這些難題均可使用量子電腦並應用秀爾演算法破解。雖然人類目前還不具備建造如此大型量子電腦的科學技術，但其安全隱患已經引起了學術研究者和政府機構的擔憂。許多密碼學家都在未雨綢繆，研發全新的公鑰加密演算法以應對將來的威脅。自第一屆後量子密碼學大會（PQCrypto）於 2006 年開辦以來，本領域的研究工作愈發活躍，已成為學術和業界的關注焦點。目前，許多學術機構、政府機構、網際網路公司都在開展研究，例如美國國家標準技術研究所（NIST）、歐洲電信標準機構（ETSI）、滑鐵盧大學量子計算研究所、Google、微軟等。
在公鑰加密方面，後量子密碼學的研究方向包括了格密碼學、容錯學習問題（LWE）、多變數密碼學、雜湊密碼學、編碼密碼學（Code-based Cryptography）與超奇異橢圓曲線同源密碼學。密碼學家認為，基於這些計算難題有望構建出不受量子電腦的威脅的公鑰加密系統，替代現有的方案。
除了公鑰加密，量子電腦也威脅對稱加密演算法和雜湊函式的安全，如 AES、SHA 等。但相比公鑰加密面臨的威脅而言，這一問題並不嚴重。藉助量子電腦，格羅弗演算法（Grover's algorithm）可將暴力破解的難度從 $N$ 次嘗試降低到 ${\sqrt {N}}$ 次嘗試。這樣，128 位元加密（金鑰空間 $2^{128}$ ）的安全性就變為 64 位元。但只需將金鑰長度提升一倍（如使用 256 位加密）即可抵抗這類攻擊。因此面臨量子電腦的威脅，公鑰加密需要重新設計，對稱加密則並不需要大幅度的修改。
為了推動標準化，NIST 在 2017 年向公眾徵集後量子密碼方案，並最終收到了各學者提交的共 69 個設計。
## 公鑰密碼學
目前，後量子公鑰密碼學的研究方向如下。
### 格密碼學 | [
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后量子密码学 | 格密碼學（Lattice-based cryptography）是在演算法構造本身或其安全性證明中應用到格的密碼學。格（lattice），又稱點陣，是群論中的數學物件，可以直觀地理解為空間中的點以固定間隔組成的排列，它具有週期性的結構。更準確地說，是在 n 維空間 Rn 中加法群的離散子群，這一數學物件有許多應用，其中存在幾個稱為「格問題」的難題，如最短向量問題（Shortest Vector Problem）和最近向量問題（Closest Vector Problem）。許多基于格的密碼系統利用到了這些難題。
經典的格密碼學加密演算法包括 GGH 加密方案（基於 CVP，已遭破解）和 NTRU 加密方案（受 GGH 啟發，基於 SVP）。由於容錯學習問題與格問題存在聯絡，因此後來基於容錯學習問題（LWE）與環容錯學習問題（Ring-LWE）的加密演算法也屬于格密碼學的範疇。
### 編碼密碼學
編碼密碼學（Code-based Cryptography）是應用了編碼理論與糾錯碼的密碼學。
其中最早、最有代表性是 McEliece 密碼系統：首先選擇一種有已知高效解碼演算法的糾錯碼作為私鑰，然後對私鑰進行轉換（用兩個隨機選擇的可逆矩陣 $S$ 與 $P$ 「打亂」糾錯碼的生成矩陣），得到公鑰。這樣，能高效解碼的特殊糾錯碼就被「偽裝」成了一般線性碼（general linear code）—— 一般線性碼的解碼十分困難，是 NP 困難問題。其密文就是引入隨機錯誤的碼字（codeword），有私鑰者可以進行糾錯得到明文，無私鑰者則無法解碼。
McEliece 演算法首次發表於 1978 年（僅比 RSA 晚一年），使用的是二元戈帕碼（Binary Goppa code），經歷了三十多年的考驗，至今仍未能破解。但缺點是公鑰體積極大，一直沒有被主串流加密法學界所採納。但隨著後量子密碼學提上日程，McEliece 演算法又重新成為了候選者。許多研究者嘗試將二元戈帕碼更換為其他糾錯碼，如里德 - 所羅門碼、LDPC 等，試圖降低金鑰體積，但全部遭到破解，而原始的二元戈帕碼仍然安全。
### 多變數密碼學 | [
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后量子密码学 | 多變數密碼學（Multivariate cryptography）是應用了有限體 $F$ 上多元多項式的密碼學，包括對稱加密和非對稱加密。當研究物件是非對稱加密時，又叫做多變數公鑰密碼學（Multivariate Public Key Cryptography），縮寫 MPKC。此外，由於它常使用二次多項式（Multivariate Quadratic），因此又可縮寫為 MQ。
考慮 $q$ 階的有限體 $F_{q}$ 。我們在其中建立一個方程組，它由 _n_ 個變數與 _m_ 個方程組成。
: ${\begin{cases}y_{1}=G_{1}(x_{1},x_{2},...,x_{n})\\y_{2}=G_{2}(x_{1},x_{2},...,x_{n})\\...\\y_{m}=G_{m}(x_{2},x_{2},...,x_{n})\\\end{cases}}$
其中每個方程式都是一個多元多項式，通常為二次多項式。
: $G_{l}(x_{1},...,x_{n})=\sum _{1\leqslant i\leqslant j\leqslant n}a_{ij}^{(l)}x_{i}x_{j}+\sum _{1\leqslant i\leqslant n}b_{i}^{(l)}x_{i}+c^{(l)}\quad (l=1,2,...,m)$
解一般形式的多元多次方程組是一個計算難題，甚至在只有二次多項式時也是如此，這就是 MQ 問題。多變數密碼學研究的就是基於這類計算難題的密碼系統。
### 雜湊密碼學
雜湊密碼學（Hash-based Cryptography）是應用雜湊函式的數位簽章。雜湊密碼學的研究歷史也很長，最早的研究工作包括萊斯利・蘭波特於 1979 年提出的蘭波特簽章（Lamport signature），與瑞夫・墨克提出的墨克樹（Merkle tree）。後來以此為基礎，又出現了 Winternitz 簽章和 GMSS 簽章，近年來的工作則包括 SPHINCS 簽章與 XMSS 簽章方案。 | [
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后量子密码学 | 雜湊密碼學的優點是：數位簽章的安全性只取決於雜湊函式，而足夠長的雜湊函式不受量子電腦威脅。其缺點是：第一，金鑰體積極大，因此一直沒有被主串流加密法學界所採納。後量子密碼學重新激發了這一領域的研究。第二，許多雜湊密碼系統的私鑰是有狀態的，簽章後都必須更新私鑰的計數器，保證同一狀態不可重用，否則簽章方案就會遭到攻擊者破解。例如，將同一私鑰同時在兩台機器上使用，就會造成巨大的安全問題。SPHINCS 簽章解決了這一問題。
### 超奇異橢圓曲線同源密碼學
超奇異橢圓曲線同源密碼學（Supersingular elliptic curve isogeny cryptography）是利用超奇異橢圓曲線與超奇異同源圖的數學性質的密碼學，可以實現超奇異同源金鑰交換（SIDH），具有前向安全性。其使用方法和現有的迪菲－赫爾曼金鑰交換相似，有望直接替代當前的常規橢圓曲線金鑰交換（ECDH）。
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] |
氪-85 | **氪 - 85** (**氪 85**) 是氪的一種放射性同位素。它的半衰期為 10.756 年，最大衰變能為 687 千電子伏特 (keV)，它衰變為穩定的銣 - 85。最常見的衰變 (99.57%) 是通過 β 粒子輻射，最大能量為 687 電子伏特，平均能量為 251 電子伏特。第二種最常見的 β 粒子輻射為 0.43% 的衰變，最大能量 173 千電子伏，其次是伽馬射線輻射 (能量為 514 千電子伏) 其他衰變模式則概率很小且輻射的伽馬射線能量也較低。
就輻射危害性而言，在不考慮氡衰變鏈其餘部分的前提下，440 貝克氪 85 相當於 1 貝克的氡 - 222。
## 大氣層中的分布
### 自然發生
氪 - 85 是由宇宙射線與大氣層中穩定的氪 - 84 相互作用產生的少量物質，自然來源在大氣層中保持著約 0.09 拍貝克的均衡量。
### 人工生產
然而，截至 2009 年，由於人為因素，大氣層中的總量估計已達到 5500 拍貝克。2000 年底，估計為 4800 拍貝克，1973 年估計為 1961 拍貝克 (53 兆居里)。這些人為來源中最重要的是核燃料再處理，核分裂每 1000 次產生約 3 個氪 - 85 原子，即裂變產出率為 0.3%。大部分或全部氪 - 85 被保留在乏核燃料棒中；從反應爐排出的乏燃料含有 0.13-1.8 拍貝克 / 毫克的氪 - 85，其中一些乏燃料會被再處理。當乏燃料溶解處理時，則會釋放氣態氪 85 到大氣中。原則上，可將這種氪氣作為核廢料收集和儲存起來，或加以利用。截至 2000 年，估計全球從再處理活動中釋放的氪 - 85 累積量為 1060 拍貝克。由於放射性衰變，上述存在於全球大氣層中的氪 - 85 量小於這一數值；只有一小部分溶解在深海中。
其他人造資源對總量作用不大，大氣層核試驗釋放了約 111-185 拍貝克；1979 年三里島核電站事故釋放了約 1.6 拍貝克 (43 千居里)；車諾比核事故釋放了大約 35 拍貝克；而福島第一核電站事故則估計釋放了 44-84 拍貝克。
1976 年，大氣層中氪 - 85 的平均濃度約為 0.6 吉貝克 / 米 3，到 2005 年已增至約 1.3 吉貝克 / 米 3，這只是近似的全球平均值；核廢料處理設施周圍的局部濃度較高，且北半球的濃度通常高於南半球。
對於廣域大氣層監測來說，氪 - 85 是反映秘密分離鈽的最佳指標。 | [
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] |
氪-85 | 氪 - 85 的釋放增加了大氣層的導電性，靠近排放源的地方，氣象影響預計會更強。
## 工業用途
氪 - 85 被用於娛樂業中常用的電弧放電燈，如大型鏑燈及高強度氣體放電燈。氙燈放電管中充入氪 - 85 使氙燈更易被點燃，早期實驗性氪 - 85 照明的開發包括 1957 年設計的鐵路信號燈和 1969 年在亞利桑那州豎立的公路照明標誌。目前隨機數伺服器 HotBits 使用了氪 - 85 封閉容器 (暗指放射性同位素是量子力學的無序狀態之源)。
氪 - 85 還用於檢查飛機部件的小缺陷，氪 - 85 能穿透小裂紋，通過放射自顯影方式檢測損傷的存在，這種方法被稱為「氪氣體滲透成像」。氣體滲透的裂口比「著色浸透探傷檢測」和「螢光滲透檢測」中使用的液體要更小。
氪 - 85 還應用於冷陰極穩壓電子管，如 5651 型。
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電化學發光 | **電化學發光**（英語：Electrochemiluminescence 或 Electrogenerated chemiluminescence）簡稱 **ECL**，是當電化學反應發生在溶液中的一種發光型式。
在電化學發光中，高放能反應中產生的反應中間體使其電子躍遷到高位能態，再到低位能態，並激發出電磁波，而發出的光子波長取決於躍遷狀態之間的間隙。 電子轉移反應（氧化還原）可以使電化學發光產生。其中一種 / 所有反應物在電極上發生電化學反應被激發的光是化學發光的形式。通常在把電動勢（幾伏特）施加到非質子有機溶劑（ECL 化合物）中包含發光物質（多環芳烴、金屬錯合物、量子點或奈米粒子）的電化學電池，其溶液的電極上可觀察到電化學發光，在有機溶劑中，通過氧化還原改變的電位差，可以在兩個電極上或在一個電極上同時產生能量來自於氧化和還原的發光物質。在主要用於分析應用的水性介質中，由於水本身的電化學分解，同時氧化和還原很難實現發光，因此使用了共反應劑進行電化學發光反應。發光物質與共反應劑一起在電極上被氧化，經過一些化學反應（氧化還原）後，共反應劑會產生強還原劑。
## 應用
電化學發光在分析應用中做為高靈敏度和選擇性的方法非常有用，它結合了化學發光分析無背景光雜訊和通過施加電壓於電極易於控制反應的優點。作為一種分析技術，由於它的多功能性，與光致發光（電磁螢光）(PL) 相比，能有較為簡化的光學設置；以及與化學發光 (CL) 相比，能有良好的時間和空間控制，其優點較其他常見分析方法的來的突出及顯著。通過改變電極電壓可以提高電化學發光分析的選擇性，從而控制在電極上氧化 / 還原並參與電化學發光反應的物質 （參見：電化學分析）。它通常使用釕化合物，特別是氯化三 (雙吡啶) 合釕 (II)（[Ru (Bpy)3]2+)（在〜620 nm 處釋放光子），並在液相或液 - 固相交界面上與三丙胺（TPrA/Tripropylamine）再生。
它可以用為例如由納菲薄膜、Langmuir-Blogett 法或自組裝技術做出的特別薄膜單層固定在電極表面，作為共反應物，通常更作為標籤。
在使用高效液相層析（HPLC），釕標記基於免疫分析上的抗體、用於聚合酶連鎖反應 (PCR) 的釕標記 DNA 探針、基於 NADH 或 H2O2 的生物傳感器、草酸鹽和有機胺檢測以及許多其他應用，並且可以從一個百萬分點濃度 (ppm) 到超過六個數量級的動態範圍進行檢測。 | [
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] |
電化學發光 | 光子檢測是透過光電倍增管（PMT）或矽光電二極體或鍍金光纖傳感器完成的。電化學發光技術檢測在生物相關應用中的重要性已得到公認 ，並且在商業上大量應用於許多臨床實驗室。
## 參見
* 生物傳感器
* 化學發光
* 電化學
* 冷發光
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自旋磁矩 | 在物理學中，主要是量子力學和粒子物理學，自旋磁矩是由基本粒子的自旋引起的磁矩。例如，電子是基本的自旋 1/2 費米子。
通常，可以根據電流和電流迴路所包圍的面積來定義磁矩。因為角動量對應於旋轉運動，所以磁矩可以與構成電流中的電荷載流子的軌道角動量有關。但是，在磁性材料中，原子偶極子和分子偶極子具有磁矩，這不僅是由於其量化的軌道角動量，還因為構成它們的基本粒子的自旋。
「自旋」是基本粒子的非經典屬性，因為從經典上講，一個物質對象的「自旋角動量」實際上只是對象成分圍繞旋轉軸_的總軌道_角動量。基本粒子被認為是沒有軸「旋轉」的點對象（請參閱波粒對偶）。
## 歷史
自旋角動量的想法最早是在 1925 年由喬治・烏倫貝克和塞繆爾・古德斯米特提提出，用於解釋原子光譜中的超精細分裂。1928 年，保羅・狄拉克用狄拉克方程為電子的波函數提供了嚴格的理論基礎。
## 自旋化學
自旋磁矩為化學中最重要的原理之一（保利排除原理）奠定了基礎。沃爾夫岡・保利（Wolfgang Pauli）首先提出的這一原理支配著當今大多數化學反應。該理論不僅在電磁譜中對雙峰的解釋中起著進一步的作用。這個額外的量子數自旋成為當今使用的現代標準模型的基礎，其中包括使用洪德規則以及對 β 衰變的解釋。
## 計算
我們可以通過以下方法計算帶有電荷 _q_ ，質量 _m_ 和自旋角動量 _S_→ 的亞原子粒子的可觀察到的自旋磁矩，矢量 _μ→_ S ，其為：
:
在哪裡是旋磁比， g 是無量綱數，稱為 g 因子， q 是電荷， m 是質量。的 α- 因子克依賴於粒子：它為 g = −2.0023 為電子 g = 5.586 對於質子，和 g = −3.826 為中子。質子和中子由的夸克，其具有非零電荷和的自旋，而這必須計算它們的 g 因子時被考慮進去。即使中子的電荷 q = 0 ，它的夸克也會給它一個磁矩。分別為 q = −1 e，其中 e 是 q = −1 e 質子和電子的自旋磁矩可以通過設定 q = 1 e 和 q = −1 e 來計算基本電荷單元。
本徵電子磁偶極矩是近似等於玻爾磁子 _B_ 因為 _g_ ≈ −2 和電子的自旋也
:
因此，等式（ 1 ）通常寫為：
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自旋磁矩 | 就像_無法測量總自旋角動量一樣，_也無法測量_總自旋磁矩_。等式（ 1 ），（ 2 ），（ 3 ）給出了沿軸相對於或沿所施加的場方向測量的磁矩的物理可觀察到的分量。假設笛卡爾坐標系，以往，與 _z_ - 軸被選擇但自旋角動量分量的沿所有三個軸的可觀察到的值分別然而，為了獲得總自旋角動量的大小 _S_→由其代替本徵值√_s_(_s_ + 1), 其中 _s_ 是自旋量子數。反過來，計算總自旋磁矩的大小要求將（ 3 ）替換為：
:
因此，對於一個單一的電子，與自旋量子數 _s_ = 1⁄2, 沿磁場方向的磁矩的組分是，從（ 3 |_μ→_S,z| = _μ_B, 而總自旋磁矩（的大小），從（ 4 |_μ→_S| = √3 _μ_B, 或約 1.73_μ_B。
分析很容易擴展到原子的自旋磁矩。例如，在封閉殼層（例如鈦 Ti 3+ 之外具有單個 d 殼層電子的過渡金屬離子的總自旋磁矩（有時被忽略了對總磁矩的軌道矩的貢獻_的有效磁矩）。_ 3+ ）是 1.73_μ_B 由於 _s_ = 1⁄2, 而具有兩個不成對電子的原子（例如釩 V3 3+ 與 _s_ = 1 將具有 2.83 _μ_B. 的有效磁矩 2.83 _μ_B.
## 相關條目
* 核磁子
* 泡利不相容原理
* 核磁共振
* 多極展開
* 相對論量子力學
* 磁自旋渦盤
## 腳註
## 參考
### 精選書籍
* B. R. Martin, G.Shaw. Particle Physics 3rd. Manchester Physics Series, John Wiley & Sons. : 5–6. ISBN 978-0-470-03294-7. 978-0-470-03294-7
* Bransden, BH; Joachain, CJ. Physics of Atoms and Molecules 1st. Prentice Hall. 1983: 631. ISBN 0-582-44401-2. 0-582-44401-2
* P.W. Atkins. Quanta: A handbook of concepts. Oxford University Press. 1974. ISBN 0-19-855493-1. 0-19-855493-1 | [
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] |
自旋磁矩 | * E. Merzbacher. Quantum Mechanics 3rd. 1998. ISBN 0-471-88702-1. 0-471-88702-1
* P.W. Atkins. Molecular Quantum Mechanics Parts I and II: An Introduction to Quantum Chemistry **1**. Oxford University Press. 1977. ISBN 0-19-855129-0. 0-19-855129-0
* P.W. Atkins. Molecular Quantum Mechanics Part III: An Introduction to Quantum Chemistry **2**. Oxford University Press. 1977. ISBN 0-19-855130-4. 0-19-855130-4
* 漢斯・科普弗曼・肯莫門_特_和_核莫蒙塔（Akademische Verl。，1940，1956，and Academic Press，1958）_
* R. Resnick; R. Eisberg. Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles 2nd. John Wiley & Sons. 1985. ISBN 978-0-471-87373-0. 978-0-471-87373-0
* Sin-Itiro Tomonaga. The Story of Spin. University of Chicago Press. 1997. ISBN 978-0-226-80794-2. 978-0-226-80794-2
### 精選論文
* Dirac, P. A. M. The Quantum Theory of the Electron. Proceedings of the Royal Society A. 1 February 1928, **117** (778): 610–624. Bibcode:1928RSPSA.117..610D. doi:10.1098/rspa.1928.0023. | [
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] |
自旋磁矩 | * Scerri, Eric R. The exclusion principle, chemistry and hidden variables. Synthese. 1995, **102** (1): 165–169. doi:10.1007/BF01063903.
## 外部連結
* Richard FW Bader 博士（麥克馬斯特大學）對原子和分子電子結構的介紹 （頁面存檔備份，存於網際網路檔案館） | [
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斯格明子 | **斯格明子**（英語：**skyrmion**）是一類非線性 sigma 模型的拓撲穩定結構，由英國物理學家托尼・斯格明於 1962 年首次提出。這種類粒子穩定場結構具有拓撲保護性質。在粒子理論中，skyrmion（/ˈskɜːrmi.ɒn/）是某類非線性 sigma 模型的拓撲穩定場構型。它最初是由 Tony Skyrme 在 1961 年提出的（並以此命名）作為核子模型。作為介子場中的拓撲孤子，它具有顯著的特性，即只需固定核子半徑，即可以合理的精度模擬核子的多種低能特性。此後，它在固態物理學中得到了應用，並與弦理論的某些領域有聯繫。
Skyrmions 作為拓撲對象在固態物理學中很重要，特別是在新興的自旋電子學技術中。二維磁性斯格明子作為拓撲對象，例如由 3D 有效自旋「刺蝟」形成（在微磁學領域：來自同倫度 +1 的所謂「布洛赫點」奇點）通過立體投影，正北極自旋映射到二維圓盤的遠處邊緣圓上，而負南極自旋映射到圓盤的中心。在旋量場中，例如光子或極化子流體，skyrmion 拓撲對應於完整的龐加萊光束 （即包含所有極化狀態的自旋量子渦旋）。
據報導，Skyrmions 存在於玻色 - 愛因斯坦凝聚體 薄磁性薄膜 和手性向列液晶 中，但尚未最終證實。
作為核子的模型，skyrmion 的拓撲穩定性可以解釋為重子數守恆的陳述；即質子不會衰變。 Skyrme Lagrangian 本質上是核子的單參數模型。修正參數修正了質子半徑，也修正了所有其他低能屬性，看起來正確到大約 30%。正是這種模型的預測能力使它作為核子模型如此吸引人。
鏤空的斯格明子構成了核子手性袋模型（柴郡貓模型）的基礎。 Dan Freed 已經獲得了費米子譜與非線性 sigma 模型的拓撲繞組數之間對偶性的精確結果。這可以解釋為對核子（但僅由夸克組成，沒有膠子）的量子色動力學（QCD）描述與核子的 Skyrme 模型之間的二元性的基礎。
斯格明子可以被量化以形成重子和共振態的量子疊加。 它可以從一些核物質特性中預測出來。
## 參見
* 粒子物理學
## 參考資料 | [
0.0886491984128952,
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] |
迪文森佐準則 | **迪文森佐準則**（DiVincenzo's criteria）是建構量子電腦的必要條件，由理論物理學家戴維・狄文森佐（David P.DiVincenzo）於 2000 年提出。量子電腦是由數學家尤里・馬寧於 1980 年以及物理學家理察・費曼於 1982 年首次提出，可作為有效模擬量子系統的工具，像是用於解決量子多體問題。
關於如何建構量子計算機的建議相當多，對於在建構量子元件時所遇到的種種挑戰，這些建議都取得了不同程度的成功。其中一些建議是使用超導量子位元、離子阱、液態和固態核磁共振或光學簇態，這些建議表明量子電腦的前景良好，但也存在阻礙其實現的問題。
迪文森佐準則由七項條件組成，實驗裝置必須符合這些條件，才得以實現如 Grover 的搜索演算法或 Shor 質因數分解演算法之類的量子演算法。前五項條件涉及量子計算本身，另外兩項條件則與實現量子通訊有關，比如量子密鑰分發中所使用的條件。我們可以證明，傳統電腦會滿足迪文森佐準則。而對傳統體系和量子體系滿足準則能力的比較，既突顯出處理量子系統時所出現的複雜性，也突顯了量子加速的起源。
## 準則說明
根據迪文森佐準則，要建造量子電腦，實驗裝置需滿足七項條件。前五項是量子電腦必要的：
1. 物理系統具有可掌控的量子位元，並具有可擴充性
2. 能夠將量子位元的狀態初始化為簡單基準狀態
3. 具有長相關退相干時間
4. 一組「通用」量子閘
5. 能夠測量特定量子位元
剩下的兩項則是量子通訊所必需的：
1. 能夠將本地量子位元和飛行量子位元互相轉換
2. 能夠準確地在兩點之間傳播飛行量子位元
## 參見
* 量子計算
* 核磁共振量子電腦
* 離子阱量子電腦
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马克斯·普朗克研究所列表 | **馬克斯・普朗克研究所**（英語：Max Planck Institutes）是指由馬克斯・普朗克學會運營的研究所，截至 2019 年 1 月 (2019-01)，總共有 86 家 ，大部分位於德國，少數位於歐洲其他國家和美國，列表如下：
* 馬克斯・普朗克演化人類學研究所（_MPI für evolutionäre Anthropologie_），萊比錫
* 馬克斯・普朗克天文學研究所（_MPI für Astronomie_），海德堡
* 馬克斯・普朗克天體物理研究所（_MPI für Astrophysik_），加興
* 赫爾奇阿娜圖書館，馬克斯・普朗克藝術史研究所（_MPI für Kunstgeschichte_），羅馬（義大利）
* 馬克斯・普朗克人類發展研究所（_MPI für Bildungsforschung_），柏林
* 馬克斯・普朗克系統動力學研究所（_MPI für Dynamik komplexer technischer Systeme_），馬格德堡
* 馬克斯・普朗克生物化學研究所（_MPI für Biochemie_），馬丁斯瑞德
* 馬克斯・普朗克生物地理化學研究所（_MPI für Biogeochemie_），耶拿
* 馬克斯・普朗克生物物理研究所（_MPI für Biophysik_），法蘭克福
* 馬克斯・普朗克血管生物學研究所（_MPI für Vaskuläre Biologie_），明斯特
* 馬克斯・普朗克化學研究所（_MPI für Chemie_，又名奧托・哈恩研究所），美因茨
* 馬克斯・普朗克生物無機化學研究所（_MPI für bioanorganische Chemie_），米爾海姆
* 馬克斯・普朗克生物物理化學研究所（_MPI für biophysikalische Chemie_，又名卡爾・弗里德里希・波恩合弗研究所），哥廷根
* 馬克斯・普朗克人口統計學研究所（_MPI für demografische Forschung_），羅斯托克
* 馬克斯・普朗克動力學和自組織研究所（_MPI für Dynamik und Selbstorganisation_，前身是馬克斯・普朗克流體研究所），哥廷根
* 馬克斯・普朗克鐵研究所公司（_Max-Planck-Institut für Eisenforschung GmbH_），杜塞道夫 | [
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马克斯·普朗克研究所列表 | * 馬克斯・普朗克實驗內分泌學研究所（_MPI für experimentelle Endokrinologie_），漢諾瓦
* 馬克斯・普朗克發育生物學研究所（_MPI für Entwicklungsbiologie_），圖賓根
* 馬克斯・普朗克蛋白質摺疊酶學研究站（_Max-Planck-Forschungsstelle für Enzymologie der Proteinfaltung_），哈雷
* 馬克斯・普朗克公共財產研究所（_MPI zur Erforschung von Gemeinschaftsgütern_），波恩
* 馬克斯・普朗克社會人類學研究所（_MPI für ethnologische Forschung_），哈雷
* 馬克斯・普朗克固體物理和材料研究所（_MPI für Festkörperforschung_），斯圖加特
* 弗雷德里希・米歇爾生物學實驗室，圖賓根
* 馬克斯・普朗克學會弗里茨・哈伯研究所（_Fritz-Haber-Institut der Max-Planck-Gesellschaft_），柏林
* 馬克斯・普朗克分子遺傳學研究所（_MPI für molekulare Genetik_），柏林
* 馬克斯・普朗克歷史研究所（_MPI für Geschichte_），哥廷根
* 馬克斯・普朗克社會研究所（_MPI für Gesellschaftsforschung_），科隆
* 馬克斯・普朗克引力物理研究所（_MPI für Gravitationsphysik_，又稱阿爾伯特・愛因斯坦研究所），波茨坦
* 馬克斯・普朗克智慧財產權、競爭法和稅收法研究所（_MPI für Geistiges Eigentum, Wettbewerbs- und Steuerrecht_），慕尼黑
* 馬克斯・普朗克腦研究所（_MPI für Hirnforschung_），法蘭克福
* 馬克斯・普朗克免疫學研究所（_MPI für Immunbiologie_），弗萊堡
* 馬克斯・普朗克傳染病生物學研究所（_MPI für Infektionsbiologie_），柏林
* 馬克斯・普朗克計算機科學研究所（_MPI für Informatik_），薩爾布呂肯
* 馬克斯・普朗克智能系統研究所（_MPI **für Intelligente Systeme**_），圖賓根 | [
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马克斯·普朗克研究所列表 | * 馬克斯・普朗克核物理研究所（_MPI für Kernphysik_），海德堡
* 馬克斯・普朗克煤炭研究所（_MPI für Kohlenforschung_），米爾海姆
* 馬克斯・普朗克膠體和界面研究所（_MPI für Kolloid- und Grenzflächenforschung_），波茨坦
* 馬克斯・普朗克生物控制學研究所（_MPI für biologische Kybernetik_），圖賓根
* 佛羅倫斯藝術史研究所，佛羅倫斯（義大利）
* 馬克斯・普朗克演化生物學研究所（_MPI für Evolutionsbiologie_），普倫
* 馬克斯・普朗克數學研究所（_MPI für Mathematik_），波恩
* 馬克斯・普朗克自然科學數學研究所（_MPI für Mathematik in den Naturwissenschaften_），萊比錫
* 馬克斯・普朗克實驗醫學研究所（_MPI für experimentelle Medizin_），哥廷根
* 馬克斯・普朗克醫學研究所（_MPI für medizinische Forschung_），海德堡
* 馬克斯・普朗克智能系統所（_MPI für Intelligente Systeme_），斯圖加特
* 馬克斯・普朗克氣象學研究所（_MPI für Meteorologie_），漢堡
* 馬克斯・普朗克海洋微生物學研究所（_MPI für marine Mikrobiologie_），不萊梅
* 馬克斯・普朗克地球微生物學研究所（_MPI für terrestrische Mikrobiologie_），馬爾堡
* 馬克斯・普朗克微結構物理學研究所（_MPI für Mikrostrukturphysik_），哈雷
* 德國電子同步加速器研究所馬克斯・普朗克結構分子生物學工作組，漢堡
* 馬克斯・普朗克神經生物學研究所（_MPI für Neurobiologie_），馬丁斯瑞德
* 馬克斯・普朗克神經學研究所（_MPI für neurologische Forschung_），科隆
* 馬克斯・普朗克認知與神經學研究所（_MPI für Kognitions- und Neurowissenschaften_），萊比錫和慕尼黑
* 馬克斯・普朗克生態化學研究所（_MPI für chemische Ökologie_），耶拿 | [
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马克斯·普朗克研究所列表 | * 馬克斯・普朗克鳥類學研究所（_MPI für Ornithologie_），許威森、安戴克斯和魯道夫澤
* 馬克斯・普朗克植物分子生理學研究所（_MPI für molekulare Pflanzenphysiologie_），波茨坦
* 馬克斯・普朗克物理學研究所（_MPI für Physik_，又稱沃納・海森堡研究所），慕尼黑
* 馬克斯・普朗克複雜系統物理研究所（_MPI für Physik komplexer Systeme_），德勒斯登
* 馬克斯・普朗克固體化學物理學研究所（_MPI für chemische Physik fester Stoffe_），德勒斯登
* 馬克斯・普朗克地外物理研究所（_MPI für extraterrestrische Physik_），加興
* 馬克斯・普朗克分子生理學研究所（_MPI für molekulare Physiologie_），多特蒙德
* 馬克斯・普朗克生理與臨床研究所（_MPI für physiologische und klinische Forschung_，又名 W.G. 凱爾克霍夫研究所），巴特諾海姆
* 馬克斯・普朗克電漿物理學研究所（_MPI für Plasmaphysik_），加興和格賴夫斯瓦爾德
* 馬克斯・普朗克聚合物研究所（_MPI für Polymerforschung_），美因茨
* 馬克斯・普朗克外國和國際民法研究所（_MPI für ausländisches und internationales Privatrecht_），漢堡
* 馬克斯・普朗克精神病理學研究所（_MPI für Psychiatrie_），慕尼黑
* 馬克斯・普朗克心理語言學研究所（_MPI für Psycholinguistik_），奈梅亨（荷蘭）
* 馬克斯・普朗克心理學研究所（_MPI für Psychologische Forschung_），慕尼黑
* 馬克斯・普朗克量子光學研究所（_MPI für Quantenoptik_），加興
* 馬克斯・普朗克無線電天文研究所（_MPI für Radioastronomie_），波恩
* 馬克斯・普朗克法律史與法理論研究所（_MPI für Rechtsgeschichte und Rechtstheorie_），法蘭克福 | [
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马克斯·普朗克研究所列表 | * 馬克斯・普朗克太陽系研究所（_MPI für Sonnensystemforschung_），卡特倫堡 - 林道
* 馬克斯・普朗克外國和國際社會法研究所（_MPI für ausländisches und internationales Sozialrecht_），慕尼黑
* 馬克斯・普朗克外國和國際刑法研究所（_MPI für ausländisches und internationales Strafrecht_），弗萊堡
* 馬克斯・普朗克比較公法與國際法研究所（_MPI für ausländisches öffentliches Recht und Völkerrecht_），海德堡
* 馬克斯・普朗克經濟系統研究所（_MPI zur Erforschung von Wirtschaftssystemen_），耶拿
* 馬克斯・普朗克科學史研究所（_MPI für Wissenschaftsgeschichte_），柏林
* 馬克斯・普朗克分子細胞生物學與遺傳學研究所（_MPI für molekulare Zellbiologie und Genetik_），德勒斯登
* 馬克斯・普朗克育種研究所（_MPI für Züchtungsforschung_），科隆
* 馬克斯・普朗克軟體系統研究所（_MPI für Softwaresysteme_），凱撒斯勞滕與薩爾布魯根
* 馬克斯・普朗克光科學研究所（_MPI für die Physik des Lichts_），埃朗根
* 馬克斯・普朗克植物育種研究所（_MPI für Pflanzenzüchtungsforschung_），科隆
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虚黑洞 | **虛黑洞**（英語：virtual black hole），量子引力中的概念，指的是由於時空無時無刻不在進行的量子真空漲落形成的微型黑洞。虛黑洞是量子泡沫的一種體現，其在萬有引力場中的作用類似於量子電動力學中的電子 - 正電子對。現有理論認為，這類黑洞的大小、壽命、質量均在普朗克尺度。
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贾拉辛斯基 | **伊戈爾・耶希耶列維奇・賈拉辛斯基**, 俄語: И́горь Ехие́льевич Дзялоши́нский, 拉丁字母轉寫: _Igor Ekhielevich Dzyaloshinskii_ 或 _Dzyaloshinsky_ ，1931 年 2 月 1 日 —2021 年 7 月 14 日，蘇聯俄羅斯理論物理學家，蘇聯科學院通訊院士，蘇聯國家獎獲得者 。
## 生平
賈拉辛斯基 1931 年生於莫斯科，1953 年畢業於莫斯科國立大學 (又譯：勒馬諾瑟夫大學，Московский государственный университет имени М. В. Ломоносова)，後前往蘇聯科學院理論物理研究所 (現朗道理論物理研究所), 1957 年博士畢業，主要研究工作為弱鐵磁（導師：朗道）。他是 朗道理論物理研究所 奠基人之一。
1974 年起，任蘇聯科學院通訊院士。自 1992 年，任加利福尼亞大學爾灣分校教授，直至榮休。
從 1958 年到 1961 年，與 阿列克謝・阿列克謝耶維奇・阿布里科索夫 和 列夫・彼得洛維奇・戈爾科夫（Лев Петрович Горьков）一起發表文章，將量子場論方法應用於統計物理（例如超導和多體理論）。此三人亦合著一著名教科書，1961 年俄語版出版，1963 年英譯版出版。 主要研究磁性相變，結晶和低維系統的統計力學。 他參與建立了多體理論中 Matsubara 表述方式 (Takeo Matsubara, 1955) 且將 Diagram 方法用於有限溫的輸運問題。
1972 年，他獲得了勒馬諾索夫獎. 1974 年成為蘇聯科學院 Sowjetischen Akademie der Wissenschaften 通訊院士。 1981 年，獲得勞動紅旗勳章。1984 年獲得蘇聯國家獎。 1989 與戈爾科夫和阿布里科索夫一同獲得朗道獎。1991 年美國藝術與科學院院士。
自 1996 年成為美國物理學會 Fellow。
2002 年美國科學促進會。
## 著作
* Abrikosov, Gorkov, Dzyaloshinskii „Quantum field theory methods in statistical physics「, Prentice Hall 1963, 2. Auflage Pergamon Press 1965, Neuauflage Dover 1977 | [
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] |
贾拉辛斯基 | * Gorkov, Abrikosov, Dzyaloshinski _On the application of Quantum field theory methods to problems of quantum statistics at finite temperature_, Sov.Phys.JETP, Bd. 9, 1959, S. 636 (JETP, Bd. 36, 1959, S. 900)
## 報導
* Abrikosov und andere: _Igor' Ekhiel'evich Dzyaloshinskii (on his seventieth birthday)_, Phys. Uspekhi, Bd. 44, 2001, S. 213
## 所獲榮譽
* 1972 — 勒馬諾索夫獎 (Mikhail Lomonosov)
* 1975 — орден «Знак Почёта»
* 1981 — 勞動紅旗勳章
* 1984 — 蘇聯國家獎 Государственной премии СССР
* 1989 — 朗道獎Премия имени Л. Д. Ландау
* 1991 — 美國藝術與科學院名譽外籍院士Американской академии искусств и наук
## 網頁連結
* Страница И. Е. Дзялошинского （頁面存檔備份，存於網際網路檔案館） на сайте Калифорнийского университета в Ирвайне（英文）
* Kurze Biographie （頁面存檔備份，存於網際網路檔案館）
* Seite beim Landau-Institut （頁面存檔備份，存於網際網路檔案館）
* Interview 2001 （頁面存檔備份，存於網際網路檔案館） (Transkription, 3 Teile)
* Template:Сотрудник РАН
* Статья （頁面存檔備份，存於網際網路檔案館） на сайте «Летопись Московского университета»
* Template:Книга:Храмов Ю. А.:Физики
## 相關條目
賈拉辛斯基 - 莫里亞 相互作用
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朗道-杨定理 | 在量子力學中，**朗道 - 楊定理**（英語：Landau–Yang theorem）是粒子衰變成兩個在殼和離殼光子的選律。該定理指出，自旋為 1 的大質量粒子不能衰變成兩個光子。
## 假設
這裡的光子是指任何自旋為 1，並且沒有質量和內部自由度的粒子。光子是唯一具有這些特性的已知粒子。
## 影響
該定理在粒子物理學中會產生幾種後果，例如：
* ρ 介子不能衰變成兩個光子，這與中性 π 介子不同，後者幾乎總是衰變成這個最終狀態（98.8% 機率）。
* W 及 Z 玻色子不能衰變為兩個光子。
* 希格斯玻色子的自旋在 2013 年以前未曾測量，但在 2012 年卻被觀察到可衰變為兩個光子，這使得在假設的朗道 - 楊定理的模型中自旋為 1 是不可能的。
## 參考資料 | [
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IBM_Q_System_One | **IBM Q System One** 是世界上第一臺商業化的量子電腦，為一台 20 量子位元（Qubits）的量子電腦，具備穩定的量子位元，不僅能在科學研究機構解決科學研究的問題，也有在商業環境下運作的可能。IBM Q System One 由 IBM 於 2019 年 1 月推出，開發團隊為 IBM 研究院。截至 2021 年 (2021-Missing required parameter 1=_month_!)，已有 150 個組織（包括學術機構、國家實驗室、新創公司、大學和企業）透過 IBM 的量子網路使用 IBM 的量子平台。
## 概要
IBM Q System One 是一台 20 量子位元（Qubits）的量子電腦，組成這臺量子電腦的量子計算系統被安裝在一個長寬高皆為 9 英尺的密封玻璃立方體中，並採用 0.5 吋厚的硼矽玻璃，以保護它的量子位元不會受到噪音和其他物理干擾的影響。
IBM Q System One 具備穩定的量子位元，不僅能在科學研究機構解決科學研究的問題，也有在商業環境下運作的可能。它的內部結構被圓柱形的黑色外殼包覆著，將裡面的零件給隱藏起來，為了方便維護，玻璃外殼也可以在維護時打開。 IBM Q System One 也相仿了傳統電腦，採用了複雜、模組化和緊湊的設計。它也透過自行設計的硬體及量子韌體，提供自動校正的功能，確保裝置的運作以及健康狀況，並達到不停機更新的目的。
## 歷史
2017 年，IBM 在消費電子展（CES）上展示了 IBM Q 量子電腦的原型機，這個原型機有 50 個量子位元，它所處的環境溫度需要下降到接近絕對零度，才能維持量子計算的穩定性。2018 年夏季，IBM 在在義大利米蘭進行了第一次 IBM Q System One 的測試。
2019 年 1 月 8 日，IBM 在消費電子展上展示了第一款商業化的量子電腦 IBM Q System One。IBM 也在該年宣布將在紐約開設首個 IBM Q 的量子計算中心。當年 4 月至 5 月，IBM 在波士頓科學博物館展示了 IBM Q System One 的複製品。 | [
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IBM_Q_System_One | 2021 年 6 月 15 日，IBM 在德國埃寧根總部安裝了 IBM Q System One 的第一個單元，並交由德國弗勞恩霍夫協會營運。這也是該公司在美國以外的地區安裝的第一台量子電腦。IBM 表示，IBM Q System One 是歐洲的工業領域中最強大的量子電腦。7 月，IBM 宣布將 Quantum System One 安裝在日本川崎市的川崎商務育成中心，日本也因此繼德國之後，成為第二個在美國以外的地區安裝 IBM 量子電腦的國家。
## 主要客戶
IBM Q System One 的主要客戶包含歐洲核子研究組織、埃克森美孚、費米實驗室、阿貢國家實驗室和勞倫斯伯克利國家實驗室。截至 2021 年 (2021-Missing required parameter 1=_month_!)，已有 150 個組織（包括學術機構、國家實驗室、新創公司、大學和企業）透過 IBM 的量子網路使用 IBM 的量子平台。
## 參見
## 參考文獻
## 外部連結
* IBM Q System One 網頁 （頁面存檔備份，存於網際網路檔案館）
* IBM Quantum Experience （頁面存檔備份，存於網際網路檔案館）
* 臺灣大學 - IBM 量子電腦中心 （頁面存檔備份，存於網際網路檔案館） | [
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私有信息檢索 | 在密碼學，**私有信息檢索**（英語：Private information retrieval，PIR）協議令用戶可以在不披露下載項目的同時，從持有資料庫的伺服器下載項目。 PIR 亦可視為一種弱化的 n 選 1 不經意傳輸（OT），但有區別，在於 OT 亦要求用戶不得獲得其他數據項目的信息。
一種平凡但效率奇低的 PIR 可以通過讓伺服器複製整個資料庫，然後傳送給用戶實現。實際上，單伺服器（不論是經典或量子）設定下，這是唯一能信息學安全地保護用戶查詢的方案。有兩種方式應對這個問題：要麼假設伺服器計算能力有限，要麼假設有若干個相互不串通的伺服器，而各伺服器持有一份資料庫的備份。
該問題的信息論版本於 1995 年由本尼・楚爾，奧德・戈德里克，埃亞爾・庫希列維茲和邁度・蘇丹引入，計算版本則於 1997 年由埃亞爾・庫希列維茲和拉斐爾・奧斯特洛夫斯基提出。之後又有研究者提出了理論上非常高效的方案。單伺服器（計算安全）PIR 只須（均攤）常數通信 ，而 _k—_ 伺服器（信息學安全）PIR 則可用 $n^{O\left({\frac {\log \log k}{k\log k}}\right)}$ 通訊完成（但下界仍然是近乎線性的量級）。
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刘文剑_(量子化学家) | **劉文劍**（1966 年 —）, 中國山東省棲霞市人，量子化學家，研究方向為量子電動力學、相對論量子力學、量子化學等。山東大學青島理論與計算科學研究院創院院長，中國教育部第四批「長江學者」特聘教授。
## 生平
1992 年獲得山東大學物理化學理學碩士學位、1995 年獲得北京大學物理化學理學博士學位；
1995 至 2001 年，先後在波鴻魯爾大學、馬克斯・普朗克物理學研究所工作；
2001 年至 2018 年任北京大學教授；
2018 年 12 月擔任山東大學講席教授。
## 學術兼職
國際量子分子科學院院士、英國皇家化學會會士、歐洲科學院院士、亞太理論與計算化學家協會會士、國際先進材料協會會士
## 參考資料
## 外部連結
* 山東大學青島理論與計算科學研究院 （頁面存檔備份，存於網際網路檔案館） | [
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] |
史蒂芬·威斯納 | **史蒂芬・威斯納**（Stephen J. Wiesner，1942 年 —2021 年 8 月 12 日），美籍以色列物理學家、發明家和建築工人。
1960 年代末和 70 年代初，於紐約哥倫比亞大學進行研究的史蒂芬・威斯納發現了量子資訊科學中幾個最重要的思想，包括量子貨幣（之後發展出量子密鑰分發）、量子多路複用和超密集編碼。儘管這些研究工作十多年來一直未正式發表，但以手稿形式廣泛傳播，刺激了 1980 年代和 90 年代量子資訊科學發展。
2006 年，史蒂芬・威斯納與查爾斯・貝內特（Charles H. Bennett）和吉勒斯・布拉薩德（Gilles Brassard） 因量子密碼學獲得蘭克獎。 2019 年，史蒂芬・威斯納與查爾斯・貝內特、吉勒斯・布拉薩德、Artur Ekert、安東・塞林格和潘建偉一起獲得墨子量子獎。
史蒂芬・威斯納移民到以色列後，成為耶路撒冷的建築工人。
## 參考資料
## 延伸資料
* _The Code Book_, Simon Singh, (Doubleday, 1999), pp. 331–338.
* _Jerry Wiesner: scientist, statesman, humanist: memories and memoirs_, Jerome Bert Wiesner and Walter A. Rosenblith, (MIT Press, 2003), p. 591.
* _Brief History of Quantum Cryptography: A Personal Perspective_, Gilles Bassard, October 17, 2005. （頁面存檔備份，存於網際網路檔案館）
* Edward Farhi, Aram Harrow. Quantum, Quantum, Quantum: Cloning, Money, and Monogamy (PDF). MIT Physics Annual Report: 59–66. 2013. （原始內容 (PDF) 存檔於 2014-12-09）. | [
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氮-空位中心 | **氮 - 空位中心** (**N-V 中心** 或 **NV 中心**)，有時也稱作 NV 色心， 是金剛石 中的一種點缺陷。 其最常被研究和應用的性質是光致發光，用以觀察其自旋狀態。氮 - 空位中心的自旋 局域在原子尺度，可以在室溫下通過外加電場、磁場、微波輻射或光來進行操控，使其光致發光強度產生共振。這些共振現象與電子自旋的量子糾纏、自旋軌道耦合和 Rabi 振盪等相關，可以用量子光學理論進行分析理解。 單個的氮 - 空位中心也可用作量子計算機的基本單元 —— 量子比特。氮 - 空位中心亦可用於自旋電子學、量子傳感等。 一般地，若提到氮 - 空位中心時沒有指定其帶電狀態，則默認所討論的是帶負電的氮 - 空位中心。
## 能級結構
NV 色心有一個三重態基態 (3A)，一個三重態激發態 (3E) 以及兩個單態中間態 (1A 和 1E)。
若沿著氮 - 空位中心的軸向加磁場 ms = 0 不受影響，但是 _m_s = ±1 的能級會發生劈裂（塞曼效應）。
## 注釋
## 參考資料 | [
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] |
三异丙胺 | **三異丙胺**是一種有機化合物，由三個異丙基和中心的一個氮原子組成。作為一種受阻的叔胺，三異丙胺可用作非親核鹼和聚合物的受阻胺類光穩定劑。然而，其應用受到其相對較高的成本和合成難度的限制。
## 結構
三異丙胺是目前已知空間位阻最大的胺之一。空間位阻更大的三叔丁胺 (tBu3N) 從未被合成，儘管量子化學從頭計算以及更擁擠的 2,2,4,4 - 四甲基 - 3 - 叔丁基 - 3 - 戊醇（三叔丁基甲醇，tBu3COH) 意味著如果它可以被製備，它應該是一個穩定的分子。至今，雙叔丁基異丙胺 (tBu2iPrN) 已經以低產率製備，其中少數的三叔丁胺中的兩個叔丁基連接在一個環中，但 2018 年的一項研究預測，合成 tBu3N 可能仍然是一個長期未解決的挑戰。
在 1990 年代初期，對分子在氣相或非極性溶劑中的 3D 結構的理論研究和電子衍射分析表明，氮原子與三個碳之間的鍵在基態時幾乎共面，而不是像更簡單的胺那樣形成三角錐形分子構型。平均 C-N-C 鍵角為 119.2°，接近於平面三角形的 120°（作為比較，三甲胺的鍵角為 111.8°）。這種特性歸因於龐大的異丙基的空間位阻。然而，1998 年的 X 射線衍射對結晶固體的分析表明，C3N 核心實際上是金字塔形的，氮原子距碳平面約 0.28 Å（而在三甲胺中，距離約為 0.45 Å）。然而，研究人員不能排除晶體場效應產生不對稱性。
異丙基的 C-C-C 平面相對於中心的 C3N 核略微傾斜（約 5°）
## 製備
位阻效應使得三異丙胺難以製備，而且不像位阻較少的叔胺（如三乙胺），它不能由氨直接被醇烷基化而成，因為反應會在二異丙胺停止。它可以從二異丙胺開始以實驗室量級製備：
:
工業生產三異丙胺涉及氨和環氧丙烷的反應，然後氫化而成。
## 參見
* 四叔丁基乙烯
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Qiskit | **Qiskit** 是一個開源軟體開發工具包 (SDK)，用於在電路、脈沖以及演算法級別運作的量子計算機上。Qiskit 提供了用於創建以及操作量子編程的能力；Qiskit 並可協助研發能在 IBM 量子體驗平台上的原型量子設備、或分散地區的計算機模擬器上產生各式運算功能的相關軟體工具。它遵循通用量子計算的電路模式，可用於遵循該模式的任何量子硬體上（目前支持超導量子位及俘獲離子等之功能）。
Qiskit 由 IBM 研究院創建研發，如上所述旨在為其雲量子計算服務的 IBM 量子體驗平台上進行軟體開發。外部的支持者也做出貢獻，通常來自學術方面等之機構。
Qiskit 的主要版本使用 Python 編程語言。最初也探索開發 Swift 及 JavaScript 等之版本，但這些版本的開發已經停止。相反地，基本功能的最小重新實作可以用 MicroQiskit 來實現，而且 MicroQiskit 也易於移植到其它的替代平台。
一系列的 Jupyter 筆記本 (Jupyter Notebook) 提供了使用量子計算的範例。範例包括使用 Qiskit 的科學研究背後之源代碼，以及一組練習題目，以之幫助人們學習量子編程的基礎知識。基於 Qiskit 的開源教科書可作為大學級別的量子演算法、或者量子計算課程等的補充教材。
## 註釋
## 參閱
* IBM 量子體驗平台
* 超導量子位
* 俘獲離子
## 外部連結
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量子編程 | **量子編程**（Quantum programming）是匯編指令序列之行程，稱為量子程序，能夠在量子計算機上運行。量子編程語言使用高級結構化的形式以助表達量子演算法的計算。
## 量子指令集
量子指令集用於將更高級別的演算法轉換為可以在量子處理器上執行的物理指令。有時這些指令是特定於給定的硬體平台，例如離子阱或超導量子位元。
### cQASM
cQASM，也稱為通用 QASM，是一種與硬體無關的 QASM，可保證所有量子編譯以及仿真工具之間的互相操作性。它是由 TUDelft 的 QCA 實驗室所引入的。
### Quil
Quil 是一種用於量子計算的指令集架構，它首先引入了共享量子 / 經典的記憶模型。它是由 "羅伯特・史密斯"(Robert Smith)、"邁克爾・柯蒂斯"(Michael Curtis)，與 "威廉・曾"(William Zeng) 在 "實用量子指令集架構"(A Practical Quantum Instruction Set Architecture) 一文中介紹的。許多量子算法（包括量子隱形傳態、量子誤差更正、模擬、以及優化演算法）需要共享記憶架構。
### OpenQASM
OpenQASM 是 IBM 引入用於 Qiskit 及 IBM 量子體驗平台的中介表示。
### Blackbird
Blackbird 是哈納杜量子技術公司及史特貝利菲爾德公司 (Strawberry Fields) 使用的量子指令集與中介所表示的。Blackbird 旨在表示可以於光子量子硬體上運行的連續可變量子程序。
## 註釋
## 延伸閱讀
## 參閱
* Quil (指令集架構)
* OpenQASM
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毎日出版文化賞 | **毎日出版文化獎**是一個每日新聞社設立的文學和社會科學獎。
## 歷史
1947 年建立，每年 11 月發布，主要獎勵在文學藝術、人文科學社會科學、自然科學和策劃等四個領域作出傑出貢獻的人才。
## 獲獎作品
### 第 1 回到第 10 回
* 第 1 回（1947 年）
* 文學・藝術部門
* 谷崎潤一郎 『細雪』
* 宮本百合子 『風知草』、『播州平野』
* 河上肇 『自敘伝』
* 人文・社會部門
* 大塚久雄 『近代歐州経済史序説』
* 田邊元 『懺悔道としての哲學』
* 戒能通孝 『入會の研究』
* 小林太市郎 『大和絵史論』
* 自然科學部門
* 久保亮五『ゴム弾性』
* 戸田盛和『液體理論』
* 緒方富雄『みんなも科學を』
* 宮本忍『気胸と成形』
* 第 2 回（1948 年）
* 文學・藝術部門
* 竹山道雄『ビルマの竪琴』
* 人文・社會部門
* 田中美知太郎『ロゴスとイデア』
* 大內力『日本資本主義の農業問題』
* 川島武宜『日本社會の家族的構成』
* 歷史學研究會『歴史學研究』
* 上原專祿『歴史的省察の新対象』
* 山田吉彥『気違い部落週遊紀行』
* 渡邊一『東山水墨畫の研究』
* 西山卯三『これからのすまい』
* 第 3 回（1949 年）
* 文學・藝術部門
* 吉川逸治『中世の美術』
* 人文・社會部門
* 西岡虎之助『民衆生活史研究』
* 遠山茂樹『世界の歴史・日本』
* 井上清『日本女性史』
* 自然科學部門
* 隈部英雄『結核の正しい知識』
* 玉木英彥『物質その究極構造』
* 松田道雄『赤ん坊の科學』
* 高森敏夫『考える子供たち』
* 古島敏雄『日本農業技術史』
* 策劃部門
* 波多野精一『波多野精一全集』
* 中島敦『中島敦全集』
* 第 4 回（1950 年）
* 文學・藝術部門
* 菊池一雄『ロダン』
* 人文・社會部門
* 南博『社會心理學』
* 小島祐馬『中國の革命思想』
* 古島敏雄『山村の構造』
* 今井譽次郎『農村社會科カリキュラムの実踐』 | [
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毎日出版文化賞 | * 農村文化協會長野県支部『明日への待望』
* 自然科學部門
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* 第 5 回（1951 年）
* 文學・藝術部門
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* 第 6 回（1952 年）
* 文學・藝術部門
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* 岡鹿之助編・撮影藤本四八『日本の彫刻』
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* 第 7 回（1953 年）
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* 第 8 回（1954 年）
* 文學・藝術部門
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* 日本応用心理學會『心理學講座』 | [
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] |
毎日出版文化賞 | * 野口彌吉『農業図説大系』
* 策劃部門
* 中教出版社『學生の理科辭典』
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* 第 9 回（1955 年）
* 文學・藝術部門
* 土門拳『室生寺』
* 中野重治『むらぎも』
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* 人文・社會部門
* 服部之總『明治の政治家たち』
* 宮澤俊義『わたくしたちの憲法』
* 自然科學部門
* 近藤康男『日本の農業』
* 岩波書店『化學の學校』
* 成瀨政男『歯車の話』
* 伊谷純一郎『高崎山のサル』
* 第 10 回（1956 年）
* 文學・藝術部門
* 前田千寸『むらさきくさ 日本色彩の文化史的研究』
* 人文・社會部門
* 岡義武『國際政治史』
* 三枝博音『日本の唯物論者』
* 杉靖三郎『人間の科學』
* 西野辰吉『秩父困民黨』
* 小西健次郎『學級革命』
* 勝田守一『お母さんから先生への百の質問』、『続お母さんから先生への百の質問』
* 自然科學部門
* 小倉金之助『近代日本の數學』
* 策劃部門
* 渡邊護『現代演奏家事典』
* 平凡社『児童百科事典』
### 第 11 回到第 20 回
* 第 11 回（1957 年）
* 文學・藝術部門
* 乾富子『ながいながいペンギンの話』
* 宮柊二『宮柊二全歌集』
* 中村吉右衛門『吉右衛門日記』
* 谷口吉郎『修學院離宮』
* 人文・社會部門
* 霜多正次『沖縄島』
* 飯塚浩二『世界と日本』
* 日本近代史研究會『寫真図説総合日本史』
* 蘆原英了『巴里のシャンソン』
* 柳田國男『綜合日本民俗語彙』
* 自然科學部門
* 伏見康治『生命の科學』
* 策劃部門
* 宮原誠一『教育學事典』
* 第 12 回（1958 年）
* 文學・藝術部門
* 神西清訳『チェーホフ戱曲集』
* 青野季吉『文學五十年』
* 遠藤周作『海與毒藥』
* 人文・社會部門
* 佐藤功『警察』
* 石光真清『城下の人』『曠野の花』
* 野上丹治『つづり方兄妹』 | [
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* 大岡昇平『花影』
* 岡本太郎『忘れられた日本』
* 柳田泉・勝本清一郎編『座談會・明治文學史』
* 大村喜吉『斎藤秀三郎伝』
* 福永武彥『ゴーギャンの世界』
* 寺村輝夫、和田誠『ぼくは王さま』
* 人文・社會部門
* 青木惠一郎『日本農民運動史』
* 自然科學部門
* 遠山啟『數學入門』
* 策劃部門
* 岡田要『原色動物大図鑑シリーズ』
* 特別獎
* 田中親美、神田喜一郎（監修）『書道全集』(全 25 巻) | [
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毎日出版文化賞 | * 檜山義夫、安田富士郎（編） 『日本水産魚譜』
* 第 16 回（1962 年）
* 文學・藝術部門
* 金田一京助『アイヌ童話集』
* 川端康成『眠れる美女』
* 喜多村綠郎『喜多村緑郎日記』
* 人文・社會部門
* 貝塚茂樹『諸子百家』
* 花田清輝『鳥獣戱話』
* 赤座憲久『目のみえぬ子ら』
* 土屋忠雄『明治前期教育政策史の研究』
* 水尾比呂志『デザイナー誕生』
* 泉靖一『インカの祖先たち』
* 日本建築協會『ふるさとのすまい』
* 特別獎
* 奈良本辰也（編集代表） 『図説日本庶民生活史』(全 8 巻)
* 第 17 回（1963 年）
* 文學・藝術部門
* 平野謙『文芸時評』
* 廣津和郎『年月のあしおと』
* 土方定一『ブリューゲル』
* 岡潔『春宵十話』
* 人文・社會部門
* 三田村泰助『宦官』
* 桂ユキ子『女ひとり原始部落に入る』
* 福武直『世界農村の旅』
* 吉澤章『たのしいおりがみ』
* 自然科學部門
* 時實利彥『脳の話』
* 桑原萬壽太郎『動物と太陽とコンパス』
* 特別獎
* 小原國芳（監修） 『玉川百科大辭典』(全 30 巻)
* 第 18 回（1964 年）
* 文學・藝術部門
* 岸本英夫『死を見つめる心』
* 北杜夫『楡家の人びと』
* 至光社『おはなしのえほん』
* 上野照夫『インドの美術』
* 青野季吉『青野季吉日記』
* 人文・社會部門
* 添田知道『演歌の明治大正史』
* 東上高志『同和教育入門』
* 藤森榮一『銅鐸』
* 自然科學部門
* 小川鼎三『醫學の歴史』
* 策劃部門
* 野上素一編『新伊和辭典』
* 特別獎
* 『毎日新聞マイクロ版』
* 林屋辰三郎・他 『光悅』
* 第 19 回（1965 年）
* 文學・藝術部門
* 望月信成・佐和隆研・梅原猛『仏像 心とかたち』
* 梅崎春生『幻化』
* 本多秋五『物語戦後文學史』
* 依田義賢『溝口健二の人と芸術』
* 小林行雄編・撮影・藤本四八『裝飾古墳』
* 人文・社會部門 | [
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] |
毎日出版文化賞 | * 永井道雄『日本の大學』
* 牧野純夫『ドルの歴史』
* 松田権六『うるしの話』
* 中根實寶子『疎開學童の日記』
* 自然科學部門
* 畑中武夫『宇宙空間への道』
* 特別獎
* 安松京三・他（編） 『原色昆蟲大図鑑』(全 3 巻)
* 第 20 回（1966 年）
* 文學・藝術部門
* 木下順二『無限軌道』
* 木戶幸一『木戸幸一日記』
* 人文・社會部門
* 兒島襄『太平洋戦爭』
* 中國新聞 (日本)『証言は消えない・広島の記録 1』、『炎の日から 20 年・広島の記録 2』、『広島の記録・年表・資料編』
* 上笙一郎・山崎朋子『日本の幼稚園』
* 歷史學研究會『日本史年表』
* 木村重信『カラハリ砂漠』
* 自然科學部門
* 藤井隆『生物學序説』
* 策劃部門
* 監修者：黒田長禮，林壽郎，八杉龍一、執筆：浦本昌紀，小原秀雄，小森厚共著『現代の記録・動物の世界』
* 特別獎
* 家永三郎・他（編） 『日本文化史』(全 8 巻)
* 橫山隆一 『勇気 橫山隆一漫畫集』
### 第 21 回到第 30 回
* 第 21 回（1967 年）
* 文學・藝術部門
* 安岡章太郎『幕が下りてから』
* 中野好夫『シェイクスピアの面白さ』
* 人文・社會部門
* 神川信彥『グラッドストン』
* 石田英一郎『マヤ文明』
* 自然科學部門
* 江上不二夫『生命を探る』
* 片山泰久『量子力學の世界』
* 策劃部門
* 藤澤衛彥『おとぎばなし』
* 戶坂潤『戸坂潤全集』
* 杉原莊介『日本の考古學』
* 特別獎
* 天理大學朝鮮學科研究室（編） 『現代朝鮮語辭典』
* 井上光貞・他 『日本の歴史』(全 26 巻)
* 文化財保護委員會（監修）、「國寶」委員會（編） 『國寶』(全 6 巻)
* 第 22 回（1968 年）
* 文學・藝術部門
* 富士正晴『桂春団治』
* 開高健『輝ける闇』
* 人文・社會部門
* 內田義彥『日本資本主義の思想像』
* 上山春平『明治維新の分析視點』
* 江上波夫『騎馬民族國家』 | [
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毎日出版文化賞 | * 本多勝一『戦場の村 ベトナム 戦爭と民衆』
* 自然科學部門
* 今堀和友『生命と分子』
* 尾川宏『紙のフォルム』
* 策劃部門
* 村松喬『教育の森』
* 特別獎
* 新世紀辭典編集部（編） 『學研新世紀大辭典』
* 第 23 回（1969 年）
* 文學・藝術部門
* 宇野重吉『新劇・愉し哀し』
* もろさわようこ『信濃のおんな』
* 杉山二郎『大仏建立』
* 坪田讓治編『びわの実學校名作選』
* 人文・社會部門
* 中野光『大正自由教育の研究』
* 三上次男『陶磁の道』
* 矢內原伊作『ジャコメッティとともに』
* 岩波書店編集部『近代日本綜合年表』
* 自然科學部門
* 海域工學研究會・合田周平編『海洋工學入門』
* 策劃部門
* 長谷川四郎『長谷川四郎作品集』
* 特別獎
* 大河內一男・他（監修） 『教育學全集』(全 15 巻)
* 久米又三・他（編） 『原色現代科學大事典』(全 10 巻)
* 第 24 回（1970 年）
* 文學・藝術部門
* 寺田透『芸術の理路 法楽帳 1968』
* 鹽野七生『チェーザレ・ボルジアあるいは優雅なる冷酷』
* 人文・社會部門
* 上田正昭『日本神話』
* 竹內好『中國を知るために』
* 北小路健『木曽路・文獻の旅』
* 北日本新聞地方自治取材班『よみがえれ地方自治』
* 宮澤俊義『天皇機関説事件』
* 自然科學部門
* 宮協昭『植物と人間 生物社會のバランス』
* なだいなだ『お醫者さん』
* 高田誠二『単位の進化』
* 特別獎
* 松永伍一 『日本農民詩史』(全 3 巻 5 冊)
* 第 25 回（1971 年）
* 文學・藝術部門
* 陳舜臣『実録アヘン戦爭』
* 堀田善衛『方丈記私記』
* 卡三吉『にんげんをかえせ・峠三吉全詩集』
* 儀間比呂志『ふなひき太良』
* 人文・社會部門
* 松下圭一『シビル・ミニマムの思想』
* 暮しの手帖編集部『からだの読本』
* 自然科學部門
* 曽田范宗『摩擦の話』
* 策劃部門 | [
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毎日出版文化賞 | * 鈴木信太郎ほか編『スタンダード和仏辭典』
* 齋藤喜博『斎藤喜博全集』
* 特別獎
* 社會科學大事典編集委員會（編） 『社會科學大事典』(全 20 巻)
* 我妻榮・他（編） 『日本政治裁判史録』(全 5 巻)
* 岩生成一・他（監修） 『大航海時代叢書』(全 11 巻・別巻 1)
* 第 26 回（1972 年）
* 文學・藝術部門
* 杉浦明平『小説渡辺崋山』
* 庄野潤三『明夫と良二』
* 服部正也『ルワンダ中央銀行総裁日記』
* 柳宗玄『ロマネスク美術』
* 島尾敏雄『硝子障子のシルエット』
* 人文・社會部門
* 福島鑄郎『戦後雑誌発掘』
* 梅原猛『隠された十字架 法隆寺論』
* 野村尚吾『伝記谷崎潤一郎』
* 兼子仁『國民の教育権』
* 自然科學部門
* 野島德吉『ワクチン』
* 特別獎
* 林達夫 『林達夫著作集』(全 6 巻)
* 細谷千博、齋藤真、今井清一、蠟山道雄（編） 『日米関係史』(全 4 巻)
* 第 27 回（1973 年）
* 文學・藝術部門
* 阿部昭『千年』
* きたむらえり『こぐまのたろ』
* 人文・社會部門
* 西川幸治『都市の思想』
* 三田博雄『山の思想史』
* 草森紳一『江戸のデザイン』
* 中井信彥『歴史學的方法の基準』
* 村松貞次郎『大工道具の歴史』
* 自然科學部門
* 辻哲夫『日本の科學思想』
* 策劃部門
* 宇井純『公開自主講座・公害原論』
* 特別獎
* 谷川健一（編集委員代表） 『日本庶民生活史料集成』(全 20 巻)
* 小田切進（編著） 『現代日本文芸総覧』(全 4 巻)
* 波多野誼余夫、稻垣佳世子『知的好奇心』
* 第 28 回（1974 年）
* 文學・藝術部門
* 城山三郎『落日燃ゆ』
* 中村真一郎『この百年の小説』
* 森蘊『庭ひとすじ』
* 人文・社會部門
* 袖井林二郎『マッカーサーの二千日』
* 宇沢弘文『自動車の社會的費用』
* 藤岡喜愛『イメージと人間』
* 自然科學部門
* 岩田久仁雄『ハチの生活』 | [
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] |
毎日出版文化賞 | * 吉川莊一『核融合への挑戦』
* 策劃部門
* 大佛次郎『天皇の世紀』
* 特別獎
* 三枝博音『三枝博音著作集』(全 12 巻)
* 丸安隆和、土屋清、中島嚴、渡邊貫太郎『日本の衛星寫真――人工衛星データの解析』
* 勝田守一『勝田守一著作集』(全 7 巻)
* 第 29 回（1975 年）
* 文學・藝術部門
* 藤村信『プラハの春モスクワの冬』
* 小松真一『虜人日記』
* 人文・社會部門
* 山崎正和『病みあがりのアメリカ』
* 色川大吉『ある昭和史』
* 山室靜『アンデルセンの生涯』
* 伊藤雅子『子どもからの自立』
* 長谷川堯『都市廻廊あるいは建築の中世主義』
* 自然科學部門
* 千葉喜彥『生物時計の話』
* 策劃部門
* 小泉明『小學館の學習百科図鑑』
* 特別獎
* 中村元『仏教語大辭典』
* 日本作文の會（編）『子ども日本風土記』(全 47 巻)
* 信多純一、齋藤清二郎（編著）『のろまそろま狂言集成――道化人形とその系譜』
* 第 30 回（1976 年）
* 文學・藝術部門
* 田久保英夫『髪の環』
* 田邊昭雄『真山青果』
* 人文・社會部門
* 堀米庸三編『西歐精神の探求』
* 富田博之『日本児童演劇史』
* 子安美知子『ミュンヘンの小學生』
* 林竹二『田中正造の生涯』
* 坂本義和『平和その現実と認識』
* 自然科學部門
* 高木貞敬『記憶のメカニズム』
* 日高敏隆『チョウはなぜ飛ぶか』
* 特別獎
* 岸本英夫『岸本英夫集』(全 6 巻)
* フランク・B・ギブニー（編） 『ブリタニカ國際大百科事典』(全 28 巻)
* 日本大辭典刊行會（編）『日本國語大辭典』（全 20 巻）
### 第 31 回到第 40 回
* 第 31 回（1977 年）
* 文學・藝術部門
* 中上健次『枯木灘』
* 山田智彥『水中庭園』
* 人文・社會部門
* 村上信彥『高群逸枝と柳田國男』
* 田岡良一『大津事件の再評価』
* 篠原一『市民參加』
* 三戸公『公と私』
* 岩田慶治『民族探検の旅』 | [
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毎日出版文化賞 | * 稻垣忠彥『アメリカ教育通信』
* 自然科學部門
* 森下郁子『川の健康診斷』
* 特別獎
* 宮崎龍介、小野川秀美（編）『宮崎滔天全集』(全 5 巻)
* 內川芳美・他（編）『現代史資料』(全 45 巻)
* 島越信（編）『日本児童文學史年表』(全 2 巻)
* 第 32 回（1978 年）
* 文學・藝術部門
* 田中千禾夫『劇的文體論序説』
* 土橋寬『萬葉開眼』
* 人文・社會部門
* 田中了『ゲンダーヌ ある北方少數民族のドラマ』
* 養護施設協議會『作文集泣くものか』
* 武田清子『天皇観の相剋 1945 年前後』
* 溪內謙『現代社會主義の省察』
* 新川明『新南島風土記』
* 自然科學部門
* 橫瀨濱三『化學症』
* 策劃部門
* 多田道太郎ほか編『クラウン仏和辭典』
* 特別獎
* 太平出版社（編） 『シリーズ・戦爭の証言』(全 20 巻)
* 梅根悟・他、世界教育史研究會（編）『世界教育史大系』(全 40 巻)
* 小田切秀雄・他（編）『小熊秀雄全集』(全 5 巻)
* 第 33 回（1979 年）
* 文學・藝術部門
* 田岡典夫『小説野中兼山』
* 人文・社會部門
* 松岡英夫『大久保一翁』
* 富岡儀八『日本の塩道 その歴史地理學的研究』
* 鶴見和子『南方熊楠』
* 渡邊京二『北一輝』
* 蘆原義信『街並みの美學』
* 自然科學部門
* 佐原雄二『さかなの食事』
* 策劃部門
* エコノミスト編集部『戦後産業史への証言』
* 特別獎
* 正木ひろし『近きより』(全 5 巻)
* 伊藤清三『日本の漆』
* 有馬澄雄（編）『水俁病――20 年の研究と今日の課題』
* 日本醫史學會（編）『図録日本醫事文化史料集成』(全 5 巻)
* 第 34 回（1980 年）
* 文學・藝術部門
* 河竹登志夫『作者の家 黙阿彌以後の人びと』
* 小池滋『英國鉄道物語』
* 中川李枝子『子犬のロクがやってきた』
* 人文・社會部門
* 小木新造『東亰時代』
* 山本市朗『北京三十五年 上下』
* 自然科學部門 | [
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毎日出版文化賞 | * 早川一光『わらじ醫者京日記』
* 策劃部門
* 吉田擴ほか『源氏物語の英訳の研究』
* 特別獎
* 田中正造全集編纂會（編）『田中正造全集』(全 19 巻・別巻)
* 半澤敏郎 『童遊文化史――考現に基づく考証的研究』(全 4 巻・別巻 1)
* 信濃教育會（編） 『一茶全集』(全 8 巻・別巻)
* 京都府醫師會.、醫學史編纂室（編）『京都の醫學史』(全 2 巻)
* 第 35 回（1981 年）
* 文學・藝術部門
* 滑川道夫『桃太郎像の変容』
* 人文・社會部門
* 日高六郎『戦後思想を考える』
* 野野山真輝帆『スペイン內戦』
* 井上千津子『ヘルパー奮戦の記』
* 自然科學部門
* 西村三郎『地球の海と生命 海洋生物地理學序説』
* 特別獎
* 田邊昭三『須恵器大成』
* 丸岡秀子・他『日本婦人問題資料集成』(全 10 巻)
* フロイス（著）、松田毅一、川崎桃太（訳）『日本史』(全 12 巻)
* 第 36 回（1982 年）
* 文學・藝術部門
* 長田弘『私の二十世紀書店』
* 人文・社會部門
* 井筒俊彥『イスラーム文化その根底にあるもの』
* 真壁仁『みちのく山河行』
* 自然科學部門
* 岡本途也編『難聴それを克服するために』
* 策劃部門
* 木村修一・足立己幸編『食塩』
* 特別獎
* 岡崎文彬『造園の歴史』(全 3 巻)
* 中本正智『図説 琉球語辭典』
* 瀨田貞二『落穂ひろい――日本の子どもの文化をめぐる人びと』(上)(下)
* 岡本茂男（寫真）、村田治郎、関野克、宇土條治（監修）『桂離宮』
* 第 37 回（1983 年）
* 文學・藝術部門
* 寺內大吉『念佛ひじり三國志 全 5 巻』
* 金田一春彥『十五夜お月さん - 本居長世 人と作品』
* 人文・社會部門
* 藤森照信『明治の東京計畫』
* 自然科學部門
* 山本高治郎『母乳』
* 策劃部門
* 井上成美伝記刊行會編『井上成美』
* 特別獎
* 日本化石集編集委員松丸國照・他（編）『日本化石集』(全 58 集・別集 1)
* 現代彫刻懇談會（編）『世界の広場と彫刻』 | [
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毎日出版文化賞 | * 沖縄大百科事典刊行事務局（編）『沖縄大百科事典』(全 3 巻・別巻 1)
* 臼井吉見・他（編）『明治文學全集』(全 99 巻)
* 第 38 回（1984 年）
* 文學・藝術部門
* 阪田寬夫『わが小林一三 清く正しく美しく』
* 人文・社會部門
* 石川榮吉『南太平洋物語』
* 細谷千博『サンフランシスコ講和への道』
* 自然科學部門
* 水野祥太郎『ヒトの足』
* 策劃部門
* 上村希美雄『宮崎兄弟伝 日本篇』
* 特別獎
* 日本兒童文學者協會（編）『県別ふるさとの民話』(全 47 巻・別巻 1)
* 戦後日本教育史料集成編集委員會（編）『戦後日本教育史料集成』(全 12 巻・別巻 1)
* 白川靜『字統』
* 第 39 回（1985 年）
* 文學・藝術部門
* 吉村典子『お産と出會う』
* 人文・社會部門
* 上田篤『流民の都市とすまい』
* 山室信一『法制官僚の時代 國家の設計と知の歴程』
* 自然科學部門
* 和秀雄『ゴンはオスでノンはメス』
* 策劃部門
* 石井威望ほか編『ヒューマンサイエンス 全 5 巻』
* 特別獎
* 鈴木竹雄、田中二郎、兼子一、石井照久（編）『法律學全集』(全 60 巻)
* 熊野正平（編）『熊野 中國語大辭典』新裝版
* 前田真三 『奧三河―前田真三寫真集』
* 鈴木重三、木村八重子、中野三敏、肥田皓三（編） 『近世子どもの絵本集』(江戸篇)(上方篇)
* 第 40 回（1986 年）
* 文學・藝術部門
* 天野忠『続天野忠詩集』
* 人文・社會部門
* 宮崎義一『世界経済をどう見るか』
* 金時鐘『「在日」のはざまで』
* 自然科學部門
* 粟津キヨ『光に向って咲け』
* 策劃部門
* 蜂谷綠『ミズハショウの花いつまでも』
* 特別獎
* 谷川健一・他六人（編） 『日本民俗文化大系』(全 14 巻)
* 八杉龍一・他五人（監修） 『現代生物學大系』(全 14 巻・別巻)
* 亞河萬里（寫真） 『イスファハン』
* 枝松茂之・他（編） 『明治ニュース事典』(全 8 巻・索引)
### 第 41 回到第 50 回 | [
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毎日出版文化賞 | * 第 41 回（1987 年）
* 文學・藝術部門
* 杉森久英『近衛文麿』
* 人文・社會部門
* 立花隆『脳死』
* 自然科學部門
* 中尾佐助『花と木の文化史』
* 策劃部門
* 武田正倫 畫・金尾恵子『干潟のカニ・シオマネキ大きなはさみのなぞ』
* 特別獎
* 安藤昌益研究會（編）『安藤昌益全集』(全 21 巻・別巻 1)
* 高木健夫（編） 『新聞小説史年表』
* 飯島春敬 『飯島春敬全集』(全 12 巻)
* 小原秀雄、浦本昌紀、內田至（編著） 『世界の天然記念物――國際保護動物』(全 9 巻)
* 第 42 回（1988 年）
* 文學・藝術部門
* 小田切秀雄『私の見た昭和の思想と文學の五十年』
* 人文・社會部門
* 山口瑞鳳『チベット』
* 橫井清『的と胞衣 中世人の生と死』
* 高柳先男『ヨーロッパの精神と現実』
* 自然科學部門
* 石弘之『地球環境報告』
* 特別獎
* 塚本洋太郎（監修）『原色茶花大事典』
* 島田修二郎、入矢義高（監修）『禪林畫賛――中世水墨畫を読む』
* 日本兒童文學學會（編）『児童文學事典』
* 第 43 回（1989 年）
* 人文・社會部門
* 犬養道子『國境線上で考える』
* 自然科學部門
* 米本昌平『遺伝管理社會 ナチスと近未來』
* 策劃部門
* 網野善彥、大西廣、佐竹昭広編『瓜と龍蛇』
* 特別獎
* 『新潮日本古典集成』(全 82 巻)
* 井上幸治、色川大吉、山田昭次（編）『秩父事件史料集成』(全 6 巻)
* 黒川洋一、入谷仙介、山本和義、橫山弘、深澤一幸（編）『中國文學歳時記』(全 7 巻)
* 第 44 回（1990 年）
* 文學・藝術部門
* 赤井達郎『京都の美術史』
* 人文・社會部門
* 山內昌之『瀕死のリヴァイアサン』
* 石田雄『日本の政治と言葉』
* 特別獎
* 塚本洋太郎（監修）『園芸植物大事典』(全 6 巻)
* 荒木博之、野村純一、福田晃、宮田登、渡辺昭五編『日本伝説大系 全 17 巻』
* 松崎次夫（編）『聞書水俁民衆史』(全 5 巻）
* 第 45 回（1991 年） | [
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毎日出版文化賞 | * 文學・藝術部門
* 中村傳三郎『明治の彫塑』
* 人文・社會部門
* 鐮田慧『六ヶ所村の記録』
* 策劃部門
* 一色八郎『箸の文化史 ［世界の箸・日本の箸］』
* 特別獎
* 西澤爽『日本近代歌謡史』(全 3 巻)
* 義太夫年表近世篇刊行會（編）『義太夫年表 近世篇』(全 5 巻・別巻 1)
* 竹內理三・他（編）『角川日本地名大辭典』(全 47 巻・別巻 2)
* 第 46 回（1992 年）
* 文學・藝術部門
* 桶谷秀昭『昭和精神史』
* 人文・社會部門
* 川田順造『口頭伝承論』
* 自然科學部門
* 河合雅雄『人間の由來』
* 特別獎
* 布目順郎『目で見る繊維の考古學――繊維遺物資料集成』
* 綱野善彥、小沢昭一、服部幸雄、宮田登、大隅和雄、山路興造編『大系日本歴史と芸能 全 14 巻』
* 矢野暢（編集代表）『講座東南アジア學』(全 10 巻・別巻 1)
* 龜井孝、河野六郎、千野榮一（編）『言語學大辭典 世界言語編』(全 4 巻)
* 第 47 回（1993 年）
* 人文・社會部門
* 青柳正規『皇帝たちの都 ローマ』
* 自然科學部門
* 中村桂子『自己創出する生命 普通と個の物語』
* 策劃部門
* 有岡利幸『松と日本人』
* 特別獎
* 藪內久『シャンソンのアーティストたち』
* 土呂久を記録する會（編）『記録・土呂久』
* 淺野建二、平井康三郎、（一部、後藤捷一）（監修）『日本わらべ歌全集』(全 27 巻)
* 天理大學、天理教道友社（共編）『ひとものこころ』(全 15 巻)
* 第 48 回（1994 年）
* 文學・藝術部門
* 阿川弘之『志賀直哉』
* 人文・社會部門
* 森田勝昭『鯨と捕鯨の文化史』
* 自然科學部門
* 今森光彥『世界昆蟲記』
* 策劃部門 （獎勵獎）
* 白幡洋三郎『プラントハンター』
* 特別獎
* 熊谷元一『熊谷元一寫真全集』(全 4 巻)
* 平山輝男（編・著）『現代日本語方言大辭典』(全 8 巻・補巻)
* 辻達也、朝尾直弘（編）『日本の近世』(全 18 巻)
* 第 49 回（1995 年） | [
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] |
毎日出版文化賞 | * 文學・藝術部門
* 佐藤忠男『日本映畫史』 全 4 巻組
* 人文・社會部門
* 福田真人『結核の文化史 - 近代日本における病のイメージ』
* 自然科學部門
* 石井謙治『和船』
* 特別獎
* 村井吉敬（代表編集）『アジアを考える本』(全 7 巻)
* 國立劇場近代歌舞伎年表編纂室（編）『近代歌舞伎年表 大阪篇』(全 9 巻)
* 中山茂（代表編集）『「通史」日本の科學技術』(全 5 巻・別巻)
* 第 50 回（1996 年）
* 文學・藝術部門
* 秋山駿『信長』
* 人文・社會部門
* 中井久夫『家族の深淵』
* 自然科學部門
* 奧利佛・薩克斯 訳・佐野正信『手話の世界へ』
* 策劃部門
* 水俁病研究會 編『水俁病事件資料集 1926-1968』全二巻組
### 第 51 回到第 60 回
* 第 51 回（1997 年）
* 人文・社會部門
* 立松和平『毒 風聞・田中正造』
* 中西輝政『大英帝國衰亡史』
* 自然科學部門
* 新妻昭夫『種の起原をもとめて ウォーレスのマレー諸島の探検』
* 策劃部門
* 田主丸町誌編集委員會 編『田主丸町誌 全 3 巻』
* 第 52 回（1998 年）
* 文學・藝術部門
* 高村薰『レディ・ジョーカー』
* 門玲子『江戸女流文學の発見 - 光ある身こそくるしき思ひなれ』
* 自然科學部門
* 岩田誠『見る脳・描く脳』
* 策劃部門
* 萱野茂編『萱野茂のアイヌ神話集成 全 10 巻』
* 第 53 回（1999 年）
* 文學・藝術部門
* 佐佐田英則訳『エリア・カザン自伝』
* 人文・社會部門
* 大林太良『銀河の道 虹の架け橋』
* 自然科學部門
* 山田真弓他監『動物系統分類學 全 10 巻』
* 策劃部門
* 作品社『日本の名隨筆 全 200 巻』
* 特別獎
* 赤瀨川原平『老人力』
* 第 54 回（2000 年）
* 文學・藝術部門
* 池澤夏樹『花を運ぶ妹』
* 人文・社會部門
* 森博達『日本書紀の謎を解く』
* 策劃部門
* 約翰・沃爾夫岡・馮・歌德（池內紀訳）『ファウスト』 | [
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] |
毎日出版文化賞 | * 谷本一之『アイヌ絵を聴く』
* 第 55 回（2001 年）
* 文學・藝術部門
* 富岡多惠子『釋迢空ノート』
* 人文・社會部門
* 原武史『大正天皇』
* 自然科學部門
* 西村肇他『水俁病の科學』
* 策劃部門
* 江戸遺蹟研究會 編『図説 江戸考古學研究事典』
* 特別賞獎
* 宮部美幸『模倣犯』
* 第 56 回（2002 年）
* 文學・藝術部門
* 石川九楊『日本書史』
* 人文・社會部門
* 唐納德・基恩『明治天皇』、角地幸男訳
* 自然科學部門
* 酒井邦嘉『言語の脳科學』
* 策劃部門
* 大塚和夫 他編『岩波イスラーム辭典』
* 特別獎
* 齋藤孝『聲に出して読みたい日本語』
* 第 57 回（2003 年）
* 文學・藝術部門
* 川本三郎『林芙美子の昭和』
* 人文・社會部門
* 小熊英二『〈民主〉と〈愛國〉』
* 綱野善彥他『日本の中世』
* 自然科學部門
* 山本義隆『磁力と重力の発見』
* 特別獎
* 養老孟司『バカの壁』
* 第 58 回（2004 年）
* 文學・藝術部門
* 阿部和重『シンセミア』
* 人文・社會部門
* 奧野正男『神々の汚れた手 文化庁・歴博関係學者の責』
* 自然科學部門
* ガブリエル・ウォーカー『スノーボール・アース』、川上紳一監修／渡會圭子訳
* 策劃部門
* 『講談社文芸文庫』、同出版部の一連の出版企畫
* 第 59 回（2005 年）
* 文學・藝術部門
* 村上龍『半島を出よ』
* 人文・社會部門
* 松本健一『若き北一輝』
* 佐藤優『國家の罠 外務省のラスプーチンと呼ばれて』
* 自然科學部門
* 中西准子『環境リスク學 不安の海の羅針盤』
* 形の科學會 編集『形の科學百科事典』
* 第 60 回（2006 年）
* 文學・藝術部門
* 保羅・克洛岱爾（渡邊守章訳）『繻子の靴』
* 人文・社會部門
* 中田整一 『満州國皇帝の秘録』
* 自然科學部門
* 高橋憲一 『ガリレオの迷宮』
* 策劃部門
* 益田勝實『益田勝実の仕事 全 5 巻』
* 特別獎 | [
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毎日出版文化賞 | * 半藤一利『昭和史』 戦前編・戦後編
### 第 61 回到第 70 回
* 第 61 回（2007 年）
* 文學・藝術部門
* 吉田修一 『悪人』
* 人文・社會部門
* 大澤真幸 『ナショナリズムの由來』
* 自然科學部門
* 松井孝典 『地球システムの崩壊』
* 策劃部門
* 鶴見祐輔 『決定版 正伝 後藤新平』（全 8 巻・別巻 1）
* 特別獎
* ドストエフスキー、訳・亀山郁夫 『カラマーゾフの兄弟』（全 5 巻）
* 第 62 回（2008 年）
* 文學・藝術部門
* 橋本治 『雙調 平家物語』（全 15 巻）
* 人文・社會部門
* 東野治之 『遣唐使』
* 自然科學部門
* 福嶌義宏 『黃河斷流―中國巨大河川をめぐる水と環境問題』
* 策劃部門
* 植木雅俊訳注 『梵漢和対照・現代語訳 法華経』（全 2 巻）
* 特別獎
* 「哲學の歴史」編集委員會編（編集委員 內山勝利、小林道夫、中川純男、松永澄夫）
『哲學の歴史』（全 12 巻・別巻 1、中央公論新社）
* 第 63 回（2009 年）
* 文學・藝術部門
* 村上春樹 『1Q84』（全 2 巻）
* 人文・社會部門
* 田中純 『政治の美學―権力と表象』
* 自然科學部門
* 藤井直敬 『つながる脳』
* 策劃部門
* 潁原退藏、編・尾形仂 『江戸時代語辭典』
* 特別獎
* 山崎豐子 『運命の人』（全 4 巻）
* 第 64 回（2010 年）
* 文學・藝術部門
* 淺田次郎 『終わらざる夏』（全 2 巻）
* 人文・社會部門
* 曽根英二 『限界集落 吾（わ）の村なれば』
* 自然科學部門
* 木村敏 『精神醫學から臨床哲學へ』
* 策劃部門
* 池澤夏樹個人編集 『河出書房新社 世界文學全集（第 1・2 期）』
* 特別獎
* 五木寬之 『親鸞』（全 2 巻）、※続編全 4 巻刊
* 第 65 回（2011 年）
* 文學・藝術部門
* 山城康治 『ドストエフスキー』
* 人文・社會部門
* 開沼博 『「フクシマ」論 原子力ムラはなぜ生まれたのか』
* 自然科學部門 | [
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毎日出版文化賞 | * 松澤哲郎 『想像するちから チンパンジーが教えてくれた人間の心』
* 策劃部門
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* 第 66 回（2012 年）
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* 日置英剛編『新・國史大年表』（全 11 冊、國書刊行會） | [
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毎日出版文化賞 | * 特別獎
* 池內恵 『イスラーム國の衝撃』（文藝春秋）
* 書評獎
* 角幡唯介 『探検家の日々本本』（幻冬舎）。
* 第 70 回（2016 年）
* 文學・藝術部門
* 島田雅彥 『虛人の星』（講談社）
* 人文・社會部門
* 鹽出浩之 『越境者の政治史』（名古屋大學出版會）
* 自然科學部門
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* 策劃部門
* 五味文彥・本鄉和人・西田友廣・遠藤珠紀・杉山嚴編『現代語訳 吾妻鏡』（全 17 冊、吉川弘文館）
* 特別獎
* 無
* 書評獎
* 荒川洋治 『過去をもつ人』（みすず書房）
### 第 71 回到第 80 回
* 第 71 回（2017 年）
* 文學・藝術部門
* 古処誠二 『いくさの底』
* 人文・社會部門
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* 自然科學部門
* 千葉聡 『歌うカタツムリ』
* 策劃部門
* 田川建三 『新約聖書 訳と註』（全 7 巻・8 冊）
* 特別獎
* 前野ウルド浩太郎 『バッタを倒しにアフリカへ』
* 第 72 回（2018 年）
* 文學・藝術部門
* 奧泉光 『雪の階』
* 人文・社會部門
* 佐藤卓己 『ファシスト的公共性－総力戦體制のメディア學』
* 自然科學部門
* 松田洋一 『性の進化史－いまヒトの染色體で何が起きているのか 』
* 策劃部門
* 內田泉之助他編 『新釈漢文大系』（全 120 巻別巻 1 完結）
* 特別獎
* 松村圭一郎 『うしろめたさの人類學 』
* 第 73 回（2019 年）
* 文學・藝術部門
* 川上未映子 『夏物語』（文芸春秋）
* 人文・社會部門
* 關根清三 『內村鑑三』（築摩書房）
* 自然科學部門
* 無
* 策劃部門
* 國分功一郎 『中動態の世界ｰ意志と責任の考古學』（醫學書院）
* 特別獎
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* 池內了 『科學者は、なぜ軍事研究に手を染めてはいけないか』（みすず書房
* 第 74 回（2020 年）
* 文學・藝術部門 | [
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] |
毎日出版文化賞 | * 藤井貞和 『＜うた＞起源考』（青土社）
* 人文・社會部門
* 苅谷剛彥 『追いついた近代 消えた近代――戦後日本の自己像と教育』（岩波書店）
* 自然科學部門
* 大熊孝 『洪水と水害をとらえなおす 自然観の転換と川との共生』（農文協プロダクション）
* 策劃部門
* 池澤夏樹個人編集 『日本文學全集』全 30 巻（河出書房新社）
* 特別獎
* 近藤讓 『ものがたり西洋音楽史』（岩波書店）
* 德丸吉彥 『ものがたり日本音楽史』（岩波書店）
## 選考委員
* 第 67 回（2013 年） - 五百旗頭真、白石太一郎、辻井喬、橋爪大三郎、林真理子、松浦壽輝、松本健一、御廚貴、村上陽一郎、養老孟司、伊藤芳明（毎日新聞社主編） ≪書評賞選考委員≫池澤夏樹、高樹信子、松原隆一郎
* 第 73 回（2019 年） - 鷲田清一、角田光代、佐伯一麥、瀧浪貞子、武田徹、中西寬、西垣通、沼野充義、小松浩（毎日新聞社主編）
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量子热力学 | **量子熱力學** 是指關於熱力學和量子力學這兩門相互獨立的物理理論間的關係的研究領域。熱力學和量子力學都討論有關光和物質的物理現象。 1905 年，阿爾伯特・愛因斯坦提出，熱力學和電磁學之間應該保持一致，由此得出了光的量子化理論，給出了 $E=h\nu $ 的關係；該論文是量子理論的曙光。幾十年過去，量子理論已經建立在另一套獨立的規則之上。 而目前，量子熱力學解決了熱力學定律怎樣從量子力學中導出的。相比於量子統計力學，量子熱力學強調從平衡態脫離的動態過程，並且試圖建立能使量子熱力學適用於單個量子系統的理論。
## 動態觀點
量子熱力學與開放量子系統密切相關。
量子熱力學用量子力學在熱力學中引入動態演化，從而為有限時間熱力學奠基。
它的主要假設是把整個世界看作閉系，從而其時間演化決定於由總哈密頓量生成的么正變換。
在熱浴模型下，組合系統的總哈密頓量可以分解為：
: $H=H_{\rm {S}}+H_{\rm {B}}+H_{\rm {SB}}$
其中 $H_{\rm {S}}$ 是系統的哈密頓量， $H_{\rm {B}}$ 是熱浴的哈密頓量， $H_{\rm {SB}}$ 是系統與熱浴的相互作用項。
系統的狀態由下列組合系統與熱浴的偏跡給出： $\rho _{\rm {S}}(t)=\mathrm {Tr} _{\rm {B}}(\rho _{\rm {SB}}(t))$ 。
系統的動力學通常只需要用系統算符描述，與此等價，也可以用約化的動力學描述整個系統的動力學。
假設系統的動力學具有馬爾可夫性質，那麼開放量子系統的基本運動方程就是 Linblad 方程 (GKLS):
: ${\dot {\rho }}_{\rm {S}}=-{i \over \hbar }[H_{\rm {S}},\rho _{\rm {S}}]+L_{\rm {D}}(\rho _{\rm {S}})$ | [
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] |
量子热力学 | 其中 $H_{\rm {S}}$ 這一部分是一個 (厄密的) 哈密頓量 ，而 $L_{\rm {D}}$ 是： $L_{\rm {D}}(\rho _{\rm {S}})=\sum _{n}\left(V_{n}\rho _{\rm {S}}V_{n}^{\dagger }-{\frac {1}{2}}\left(\rho _{\rm {S}}V_{n}^{\dagger }V_{n}+V_{n}^{\dagger }V_{n}\rho _{\rm {S}}\right)\right)$
## 參見
* 熱量子場論
* 量子統計力學
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四维梯度 | 在微分幾何中，四維梯度（或 4 - 梯度，4-gradient） ${\displaystyle \mathbf {\partial } }$ 是向量微積分中的梯度 ${\displaystyle {\vec {\mathbf {\nabla } }}}$ 在四維矢量中的推廣。
在狹義相對論和量子力學中，4 - 梯度用於定義各種 4 - 向量和張量形式的物理量之間的性質和關係。
## 記號說明
使用四維梯度時應註明度規。下文使用的度規號差是 (+,-,-,-)。
縮寫 SR 和 GR 分別代表狹義相對論和廣義相對論。_c_ 表示真空中的光速。 ${\displaystyle \eta _{\mu \nu }=\operatorname {diag} [1,-1,-1,-1]}$ 是 SR 的平坦時空度規。
物理學中表記含有 4 - 矢量的表達式，通常有下列兩種寫法：
* 4 - 矢量樣式： ${\displaystyle \mathbf {A} \cdot \mathbf {B} }$ 。通常更緊湊，可以使用一般的向量記號（例如內積「點」），始終使用粗體大寫字母表示 4 - 矢量量，用粗體小寫字母表示三維空間矢量，如 ${\displaystyle {\vec {\mathbf {a} }}\cdot {\vec {\mathbf {b} }}}$ 。多數三維空間矢量的規則在四矢量數學中都有其對應。
* 里奇代數的樣式： ${\displaystyle A^{\mu }\eta _{\mu \nu }B^{\nu }}$ 。它使用張量的抽象指標記號，便於書寫更複雜的表達式，尤其是對於涉及多個指標維度的張量表達式，如 ${\displaystyle F^{\mu \nu }=\partial ^{\mu }A^{\nu }-\partial ^{\nu }A^{\mu }}$ .
這裡，用帶拉丁字母張量指標的字母表示三維空間向量，指標取值範圍是 {1, 2, 3}, 如 ${\displaystyle A^{i}=\left(a^{1},a^{2},a^{3}\right)={\vec {\mathbf {a} }}}$ . | [
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四维梯度 | 用帶希臘字母的張量指標的字母表示 4 - 矢量，指標取值範圍在 {0, 1, 2, 3}, 如 ${\displaystyle A^{\mu }=\left(a^{0},a^{1},a^{2},a^{3}\right)=\mathbf {A} }$ .
在 SR 中，為了簡潔，通常會混用以上兩種樣式，如寫作 ${\displaystyle \mathbf {A} =\left(a^{0},{\vec {\mathbf {a} }}\right)}$ ， 用 ${\displaystyle a^{0}}$ 表示時間分量，卻用 ${\displaystyle {\vec {\mathbf {a} }}}$ 表示空間的三維分量。
SR 中的張量通常是 4 維 (m,n)- 張量，具有 m 個上指標和 n 個下指標，每個指標的取值範圍有四個值。
Minkowski 度規中使用的張量縮並可以寫在任意一邊（參見愛因斯坦求和約定）： : ${\displaystyle \mathbf {A} \cdot \mathbf {B} =A^{\mu }\eta _{\mu \nu }B^{\nu }=A_{\nu }B^{\nu }=A^{\mu }B_{\mu }=\sum _{\mu =0}^{3}a^{\mu }b_{\mu }=a^{0}b^{0}-\sum _{i=1}^{3}a^{i}b^{i}=a^{0}b^{0}-{\vec {\mathbf {a} }}\cdot {\vec {\mathbf {b} }}}$
## 定義
4 - 梯度的協變分量用 4 - 矢量和里奇代數表示法中的簡略寫法有：
$$ | [
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四维梯度 | {\displaystyle {\dfrac {\partial }{\partial X^{\mu }}}=\left(\partial _{0},\partial _{1},\partial _{2},\partial _{3}\right)=\left(\partial _{0},\partial _{i}\right)=\left({\frac {1}{c}}{\frac {\partial }{\partial t}},{\vec {\nabla }}\right)=\left({\frac {\partial _{t}}{c}},{\vec {\nabla }}\right)=\left({\frac {\partial _{t}}{c}},\partial _{x},\partial _{y},\partial _{z}\right)=\partial _{\mu }={}_{,\mu }}
$$
上式最後一部分中，逗號 ${\displaystyle {}_{,\mu }}$ 指的是關於 4 - 位置 ${\displaystyle X^{\mu }}$ 的偏微分 .
它的逆變分量是：
$$
{\displaystyle \mathbf {\partial } =\partial ^{\alpha }=\eta ^{\alpha \beta }\partial _{\beta }=\left(\partial ^{0},\partial ^{1},\partial ^{2},\partial ^{3}\right)=\left(\partial ^{0},\partial ^{i}\right)=\left({\frac {1}{c}}{\frac {\partial }{\partial t}},-{\vec {\nabla }}\right)=\left({\frac {\partial _{t}}{c}},-{\vec {\nabla }}\right)=\left({\frac {\partial _{t}}{c}},-\partial _{x},-\partial _{y},-\partial _{z}\right)}
$$ | [
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四维梯度 | ${\displaystyle \partial _{\alpha }}$ 也寫作 ${\displaystyle \Box }$ 或者 D （不過 ${\displaystyle \Box }$ 也有可能表示達朗貝爾算子 ${\displaystyle \partial ^{\mu }\partial _{\mu }}$ ）。
在 GR 中，必須使用更通用的度規張量 ${\displaystyle g^{\alpha \beta }}$ ，以及張量協變導數 ${\displaystyle \nabla _{\mu }={}_{;\mu }}$ （不要與矢量的 3 - 梯度 ${\displaystyle {\vec {\nabla }}}$ 混淆）。這裡，協變導數 ${\displaystyle \nabla _{\nu }}$ 是 4 - 梯度 ${\displaystyle \partial _{\nu }}$ 加上時空曲率效應（用 Christoffel 符號 ${\displaystyle \Gamma ^{\mu }{}_{\sigma \nu }}$ 表出）。
強等效原理可以表述為：
「SR 中任意可用張量記號表示的物理定律，在彎曲時空的局部慣性系中，都具有完全相同的形式。」 其中需要把 SR 中的 4 - 梯度逗號 (,) 替換成 GR 中的協變導數分號 (;)，這兩格微分算符之間可以通過 Christoffel 符號相互變換。在相對論物理學中稱之為「逗號換成分號規則」。
所以，例如，如果在 SR 中有 ${\displaystyle T^{\mu \nu }{}_{,\mu }=0}$ ，那麼在 GR 中有 ${\displaystyle T^{\mu \nu }{}_{;\mu }=0}$ 。
對於 (1,0)- 張量或 4 - 矢量，此規則化簡為：
$$
{\displaystyle {\begin{aligned}\nabla _{\beta }V^{\alpha }&=\partial _{\beta }V^{\alpha }+V^{\mu }\Gamma ^{\alpha }{}_{\mu \beta }\\V^{\alpha }{}_{;\beta }&=V^{\alpha }{}_{,\beta }+V^{\mu }\Gamma ^{\alpha }{}_{\mu \beta }\end{aligned}}} | [
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四维梯度 | $$
對於 (2,0)- 張量，該規則化簡為：
$$
{\displaystyle {\begin{aligned}\nabla _{\nu }T^{\mu \nu }&=\partial _{\nu }T^{\mu \nu }+\Gamma ^{\mu }{}_{\sigma \nu }T^{\sigma \nu }+\Gamma ^{\nu }{}_{\sigma \nu }T^{\mu \sigma }\\T^{\mu \nu }{}_{;\nu }&=T^{\mu \nu }{}_{,\nu }+\Gamma ^{\mu }{}_{\sigma \nu }T^{\sigma \nu }+\Gamma ^{\nu }{}_{\sigma \nu }T^{\mu \sigma }\end{aligned}}}
$$
## 用途
4 - 梯度在狹義相對論（SR）中有多處應用：
下面的公式都是針對 SR 的平直時空閔氏時空坐標所寫，對於廣義相對論 GR 中推廣了的彎曲時空坐標，需要加以調整修改。
### 用作 4 - 散度以及守恆律中的源
散度這個矢量算符作用在矢量場上時就給出一個區分正負號的純量場，大小是矢量場在空間個點上的流的源或者匯。
4 - 位置 $X^{\mu }=\left(ct,{\vec {\mathbf {x} }}\right)$ 的 4 - 散度給出了時空的維度： $\mathbf {\partial } \cdot \mathbf {X} =\partial ^{\mu }\eta _{\mu \nu }X^{\nu }=\partial _{\nu }X^{\nu }=\left({\frac {\partial _{t}}{c}},-{\vec {\nabla }}\right)\cdot (ct,{\vec {x}})={\frac {\partial _{t}}{c}}(ct)+{\vec {\nabla }}\cdot {\vec {x}}=(\partial _{t}t)+(\partial _{x}x+\partial _{y}y+\partial _{z}z)=(1)+(3)=4$ | [
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四维梯度 | 4 - 電流密度 $J^{\mu }=\left(\rho c,{\vec {\mathbf {j} }}\right)=\rho _{o}U^{\mu }=\rho _{o}\gamma \left(c,{\vec {\mathbf {u} }}\right)=\left(\rho c,\rho {\vec {\mathbf {u} }}\right)$ 的 4 - 散度給出一個守恆律，即電荷守恆律：
: $\mathbf {\partial } \cdot \mathbf {J} =\partial ^{\mu }\eta _{\mu \nu }J^{\nu }=\partial _{\nu }J^{\nu }=\left({\frac {\partial _{t}}{c}},-{\vec {\nabla }}\right)\cdot (\rho c,{\vec {j}})={\frac {\partial _{t}}{c}}(\rho c)+{\vec {\nabla }}\cdot {\vec {j}}=\partial _{t}\rho +{\vec {\nabla }}\cdot {\vec {j}}=0$
這就是說，電荷密度的時間變化率必定等於負的電流密度的空間散度： $\partial _{t}\rho =-{\vec {\nabla }}\cdot {\vec {j}}$ .
換言之，任取一個方盒區域，其中的電荷量的變化必須通過進出盒子的電流，而不能憑空變化。上述方程屬於是連續性方程。
4 - 粒子數通量（4-number flux，4-dust） $N^{\mu }=\left(nc,{\vec {\mathbf {n} }}\right)=n_{o}U^{\mu }=n_{o}\gamma \left(c,{\vec {\mathbf {u} }}\right)=\left(nc,n{\vec {\mathbf {u} }}\right)$ 的 4 - 散度可用於粒子數守恆： | [
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四维梯度 | : $\mathbf {\partial } \cdot \mathbf {N} =\partial ^{\mu }\eta _{\mu \nu }N^{\nu }=\partial _{\nu }N^{\nu }=\left({\frac {\partial _{t}}{c}},-{\vec {\nabla }}\right)\cdot \left(nc,n{\vec {\mathbf {u} }}\right)={\frac {\partial _{t}}{c}}\left(nc\right)+{\vec {\nabla }}\cdot n{\vec {\mathbf {u} }}=\partial _{t}n+{\vec {\nabla }}\cdot n{\vec {\mathbf {u} }}=0$
這是粒子數密度的守恆律，典型的比如重子數密度。
電磁 4 - 勢 $A^{\mu }=\left({\frac {\phi }{c}},{\vec {\mathbf {a} }}\right)$ 的 4 - 散度則用於洛倫茲規範條件：
: $\mathbf {\partial } \cdot \mathbf {A} =\partial ^{\mu }\eta _{\mu \nu }A^{\nu }=\partial _{\nu }A^{\nu }=\left({\frac {\partial _{t}}{c}},-{\vec {\nabla }}\right)\cdot \left({\frac {\phi }{c}},{\vec {a}}\right)={\frac {\partial _{t}}{c}}\left({\frac {\phi }{c}}\right)+{\vec {\nabla }}\cdot {\vec {a}}={\frac {\partial _{t}\phi }{c^{2}}}+{\vec {\nabla }}\cdot {\vec {a}}=0$
這等價於電磁 4 - 勢對應的守恆律。
弱場極限（即，遠離場源的自由傳播條件）下的引力輻射可以表示為一個橫向無跡的 4D (2,0)- 張量 $h_{TT}^{\mu \nu }$ ，它的 4 - 散度 | [
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四维梯度 | : $\mathbf {\partial } \cdot h_{TT}^{\mu \nu }=\partial _{\mu }h_{TT}^{\mu \nu }=0$ ：橫向條件
等價於自由傳播的引力波的守恆方程。
應力 - 能量張量 $T^{\mu \nu }$ 的 4 - 散度是與時空有關的守恆的諾特流，在 SR 中，它給出四條守恆律：
能量守恆（時間方向）和線性動量的守恆（三個獨立的空間方向）：
$$
\mathbf {\partial } \cdot T^{\mu \nu }=\partial _{\nu }T^{\mu \nu }=T^{\mu \nu }{}_{,\nu }=0^{\mu }=(0,0,0,0)
$$
這通常寫作：
$$
\partial _{\nu }T^{\mu \nu }=T^{\mu \nu }{}_{,\nu }=0
$$
當然，這裡的 0 是指一個 4 - 矢量 $0^{\mu }=(0,0,0,0)$ 。
把理想流體的應力 - 能量張量守恆（ $\partial _{\nu }T^{\mu \nu }=0^{\mu }$ ）與粒子數守恆（ $\mathbf {\partial } \cdot \mathbf {N} =0$ ）結合起來，可以推出相對論性歐拉方程，用來研究流體力學和天體物理學中的狹義相對論效應。
在流體的三維空間速度遠小於光速、壓強遠小於能量密度、能量密度主要由靜止質量密度貢獻的經典極限下，上述方程退化為經典歐拉方程。
在平直時空下，用笛卡爾坐標，結合壓強 - 能量張量的對稱性，即可證明相對論性角動量也是守恆的：
: $\partial _{\nu }\left(x^{\alpha }T^{\mu \nu }-x^{\mu }T^{\alpha \nu }\right)=\left(x^{\alpha }T^{\mu \nu }-x^{\mu }T^{\alpha \nu }\right)_{,\nu }=0^{\alpha \mu }$
這裡的零是 (2,0)- 張量的零。
## 參見
* 四維矢量
* 四維速度
## 參考
## 延伸閱讀
* S. Hildebrandt, "Analysis II" (Calculus II), ISBN 3-540-43970-6, 2003 | [
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] |
四维梯度 | * L.C. Evans, "Partial differential equations", A.M.Society, Grad.Studies Vol.19, 1988
* J.D. Jackson, "Classical Electrodynamics" Chapter 11, Wiley ISBN 0-471-30932-X | [
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] |
克勞斯·哈塞爾曼 | **克勞斯・哈塞爾曼**（德語：Klaus Hasselmann，1931 年 10 月 25 日 —），德國海洋學家、氣候建模師。知名研究成果為展現氣候變異的「哈塞爾曼模型」，該系統擁有長期相依性（海洋），整合了隨機強迫，從而將白噪聲訊號轉換為紅噪聲訊號，以此解釋（無需特殊假設）氣候中無處不在的紅噪聲訊號。2021 年，哈塞爾曼與真鍋淑郎一同獲得諾貝爾物理學獎，以表彰他們對「建構物理形式的地球氣候模型，量化可變性並確切地預測全球暖化」所做的突破性貢獻。
## 生平
哈塞爾曼生於威瑪共和國時期的漢堡，父親埃爾溫・哈塞爾曼是經濟學家、記者兼出版商，1920 年代活躍於德國社會民主黨。1934 年中旬，希特勒掌權納粹德國，哈塞爾曼舉家搬到英國，逃離納粹對社會民主黨人的鎮壓，當時哈塞爾曼兩歲。一家人住在倫敦北部的韋林花園市，父親做起了記者。雖然哈塞爾曼一家不是猶太人，但在貴格會的幫助下抵達英國，之後住在多為猶太裔德國移民的社群。克勞斯・哈塞爾曼就讀於韋林花園市小學與文法學校（Elementary and Grammar School），1949 年通過 A-level 考試獲得劍橋高中憑證。哈塞爾曼在英國過得開心，而英語也成了他的第一語言。1948 年，一家人回到漢堡，克勞斯則留在英國完成 A-level 課程。1949 年 8 月，將滿 18 歲的哈塞爾曼隨父母回到西德，完成高等教育。1949 年至 1950 年參加機械工程實踐課程後，他於 1950 年進入漢堡大學學習物理和數學。
1955 年，哈塞爾曼獲漢堡大學物理學與數學文憑，1957 年在哥廷根大學和馬克斯・普朗克流體動力學研究所獲得物理學博士學位，1964 年至 1975 年擔任漢堡大學地球物理研究所所長兼理論地球物理學全職教授。
1975 年 2 月至 1999 年 12 月，任漢堡馬克斯・普朗克氣象研究所創始所長。1988 年 1 月至 1999 年 11 月，任德國氣候計算中心科學主任。現任歐洲氣候論壇副主席。
哈塞爾曼論文課題包括氣候動力、隨機過程、海浪、遙感和綜合評估研究。
通過一連串研究海浪非線性互動的論文，哈塞爾曼在海洋學建立了一定的聲譽。他在論文中將費曼圖的形式主義應用於經典隨機波場。後來，他發現電漿體物理學家正把類似的技術應用於電漿體波，重新發現了魯道夫・佩爾斯一些通過非線性聲子相互作用解釋固體中的熱量擴散的結果。這個發現讓他重新審視電漿體物理學領域，重燃早前對量子場論的興趣。 | [
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] |
克勞斯·哈塞爾曼 | 1971 年，哈塞爾曼獲美國氣象學會斯沃卓普獎章（Sverdrup Medal），1997 年獲皇家氣象學會西蒙斯紀念獎章（Symons Memorial Medal），2002 年 4 月獲歐洲氣象物理學會威廉・皮耶克尼斯獎章，2009 年獲 BBVA 基金會知識前沿獎氣候變遷獎。
克勞斯・哈塞爾曼與妻子蘇珊娜於 1957 年結婚，兩人是馬克斯・普朗克氣象研究所的同事，育有三個孩子。
## 著作
* M. Welp, K. Hasselmann, C. Jaeger, Climate Change and Paths to Sustainability: the Role of Science- Based Stakeholder Dialogues （頁面存檔備份，存於網際網路檔案館）, The Environment
* Barnett, Tim; Zwiers, Francis; Hengerl, Gabriele; Allen, Myles; Crowly, Tom; Gillett, Nathan; Hasselmann, Klaus; Jones, Phil; Santer, Ben; Schnur, Reiner; Scott, Peter; Taylor, Karl; Tett, Simon. Detecting and Attributing External Influences on the Climate System: A Review of Recent Advances. Journal of Climate (American Meteorological Society). 2005-05-01, **18** (9): 1291–1314. ISSN 1520-0442. doi:10.1175/jcli3329.1. | [
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] |
克勞斯·哈塞爾曼 | * K. Hasselmann, Climate-change research after Kyoto, Nature, 390, 225–226, 1997
* K. Hasselmann, Are We Seeing Global Warming? （頁面存檔備份，存於網際網路檔案館）, Science, 276, 914–915, 1997
完整列表參見「Interview mit Klaus Hasselmann」, 59, 2006. 或哈塞爾曼在馬克斯・普朗克氣象研究所網站的履歷
## 參考資料
## 外部連結
* 個人官方網站
* 歐洲氣候論壇 （頁面存檔備份，存於網際網路檔案館）
* 德國氣候和地球系統研究高效能計算中心 （頁面存檔備份，存於網際網路檔案館）
* 克勞斯・哈塞爾曼在數學譜系計畫的資料。 | [
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卡迪森－辛格問題 | 數學上，**卡迪森 - 辛格問題**（英語：Kadison–Singer problem）於 1959 年提出，有關泛函分析，問某個特定 C\*- 代數上的任意線性泛函，延拓到另一個較大的 C\*- 代數時，是僅有唯一的可能，抑或可以有多個不同的延拓。2013 年，問題得到解決，答案為肯定（即唯一）。
問題源出 1940 年代保羅・狄拉克對量子力學理論基礎的研究。1959 年，理察・卡迪森與艾沙道爾・辛格給出嚴格的問題敍述。此後，發現純數學、應用數學、工程學、電腦科學等學科的多個未解問題，皆與卡迪森 - 辛格問題等價。卡迪森、辛格，以及日後多個作者，都相信問題答案為否定（即不唯一），然而於 2013 年，亞當・馬庫斯、丹尼爾・斯皮爾曼、尼基・斯里瓦斯塔瓦合著論文給出肯定的答案。翌年，三人因此獲 SIAM 頒發波利亞獎。
馬 - 斯 - 斯三氏皆為電腦科學家，本來並非研究 C\*- 代數。馬庫斯甚至稱自己在解決該問題後，「仍無法用 C\*- 代數的語言來描述它」。解決問題的轉捩點，是喬爾・安德森（Joel Anderson）將其重寫成不牽涉 C\*- 代數理論的等價形式。安德森於 1979 年證明，其「鋪砌猜想」（英語：paving conjecture）與卡迪森 - 辛格問題等價。該猜想僅牽涉有限維希爾伯特空間的算子，而相比之下，原問題的空間則是無窮維。此後，亦有其他學者，如尼克・威佛（Nik Weaver），在有限維空間中，給出其他等價問法。威佛的版本吸引了馬 - 斯 - 斯三氏研究。而此版本用交織多項式族（英語：interlacing family）獲解決。
## 原問題敍述
先引入若干定義：
**${\boldsymbol {\ell }}^{2}$**
: 平方可和的複序列空間，即 $\ell ^{2}=\left\{(x_{1},x_{2},\ldots ):x_{i}\in \mathbb {C} ,\sum _{i}\left|x_{i}\right|^{2}<\infty \right\}$ 。此空間為可分希爾伯特空間，內積定義由 $\langle x,y\rangle =\sum _{i}x_{i}{\overline {y_{i}}}$ 給出。
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] |
卡迪森－辛格問題 | : 從 $\ell ^{2}$ 到 $\ell ^{2}$ 的連續線性算子組成的集合。此集合上，有加減法、乘法、伴隨等運算，構成一個 C\*- 代數。
**${\boldsymbol {D}}({\boldsymbol {\ell }}^{2})$**
: 從 $\ell ^{2}$ 到 $\ell ^{2}$ 的對角連續線性算子集合。換言之， $D(\ell ^{2})=\left\{\left.f:\ell ^{2}\to \ell ^{2}\right|f(x)=(a_{1}x_{1},a_{2}x_{2},\ldots ),{\text{ 其 中 }}a_{i}\in \mathbb {C} ,{\text{ 且 }}a_{i}{\text{ 有 界 }}\right\}$ 。 $D(\ell ^{2})$ 包含於 $B(\ell ^{2})$ ，故為其子 C\*- 代數。
**態**
: C\*- 代數 $A$ 上的態，是連續線性泛函 $\varphi :A\to \mathbb {C} $ ，將單位元 $I$ 映到 $1$ ，且對任意半正定的 $T\geq 0$ ，有 $\varphi (T)\geq 0$ （即此時 $\varphi (T)$ 要取實值，且該實值為非負）。
**純態**
: 接續上項， $\varphi $ 稱為純態，意思是在 $A$ 上所有態組成的集合中， $\varphi $ 是極端點，即不能寫成其他態的凸組合。
由哈恩 - 巴拿赫定理， $D(\ell ^{2})$ 上的任意泛函，必能延拓到 $B(\ell ^{2})$ 上。卡迪森與辛格二人問，對於純態，此延拓是否唯一。所以，卡迪森 - 辛格問題是要證明或否證以下命題：
> 對 $D(\ell ^{2})$ 上的任意純態 $\varphi $ ， $B(\ell ^{2})$ 上都存在唯一的態 $\psi $ ，使 $\psi $ 延拓 $\varphi $ ，即兩者限制到 $D$ 時等同。
>
>
此命題已證為真。
## 鋪砌猜想敍述
卡迪森 - 辛格問題的答案為肯定，當且僅當以下**鋪砌猜想**為真： | [
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] |
卡迪森－辛格問題 | > 對任意的 $\varepsilon >0$ ，存在正整數 $k$ 使得：對每個 $n$ ，以及對 $n$ 維希爾伯特空間 $\mathbb {C} ^{n}$ 上的每個線性算子 $T$ （可視為 $n\times n$ 方陣），若其對角線全零，則存在某種方法將 $\{1,\dots ,n\}$ 分劃為 $k$ 份 $A_{1},\dots ,A_{k}$ ，使得
>
>
> : : $\|P_{A_{j}}TP_{A_{j}}\|\leq \varepsilon \|T\|$ 對於每個 $j=1,\ldots ,k$ 都成立。
>
> 此處 $P_{A_{j}}$ 是正交投影，將 $\mathbb {C} ^{n}$ （坐標以 $1,2,\ldots ,n$ 為下標）映到坐標僅以 $A_{j}$ 元素為下標的子空間。換言之， $P_{A_{j}}TP_{A_{j}}$ 是下標為 $A_{j}$ 元素的各行列，相交而得的子方陣。而矩陣範數 $\|\cdot \|$ 取為譜範數，即來自 $\mathbb {C} ^{n}$ 上歐氏範數的算子範數。
>
>
注意命題中， $k$ 只能與 $\varepsilon $ 有關，但不取決於 $n$ 。
## 偏差敍述
尼克・威佛（Nik Weaver）證明，以下「偏差理論」命題，同樣與卡迪森 - 辛格問題（的肯定答案）等價：
> 設有向量 $u_{1},\ldots ,u_{m}\in \mathbb {C} ^{d}$ ，滿足 $\sum _{i=1}^{m}u_{i}u_{i}^{*}=I$ （ $d\times d$ 單位方陣），且對每個 $i$ ， $\|u_{i}\|_{2}^{2}\leq \delta $ 。則存在一種方法將 $\{1,\ldots ,m\}$ 分劃成兩個子集 $S_{1}$ 和 $S_{2}$ ，使得對於 $j=1,2$ 都有
>
>
> : $\left\|\sum _{i\in S_{j}}u_{i}u_{i}^{*}\right\|\leq {\frac {\left(1+{\sqrt {2\delta }}\right)^{2}}{2}}.$
>
>
馬庫斯、斯皮爾曼、斯里瓦斯塔瓦三人用交織多項式族（英語：interlacing families）的技巧，證明上述命題為真。該命題又有以下推論：
> | [
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] |
卡迪森－辛格問題 | > 設向量 $v_{1},\ldots ,v_{m}\in \mathbb {R} ^{d}$ 滿足 $\|v_{i}\|_{2}^{2}\leq \alpha $ （對所有 $i$ ），還有
>
>
> : $\sum _{i=1}^{m}\langle v_{i},x\rangle ^{2}=1$ 對滿足 $\|x\|=1$ 的所有向量 $x\in \mathbb {R} ^{d}$ 成立。
>
> 則可以將 $\{1,\ldots ,m\}$ 分劃成兩個子集 $S_{1}$ 、 $S_{2}$ ，使得對 $j=1,2$ ，以及滿足 $\|x\|=1$ 的任意向量 $x\in \mathbb {R} ^{d}$ ，皆有：
>
>
> : $\left|\sum _{i\in S_{j}}\langle v_{i},x\rangle ^{2}-{\frac {1}{2}}\right|\leq 5{\sqrt {\alpha }}.$
>
>
「偏差」一詞的含義，在 $\alpha $ 較小時顯明：在單位球面上取值恆為 $1$ 的二次型，可以分拆成兩個大致相等的二次型，而分拆出來的二次型在單位球面上各處的取值，離 $1/2$ 的偏差很小。利用命題此種形式，可以推導出關於圖分劃的若干結果。
## 參考文獻
## 外部鏈結
* Nicholas J. A. Harvey. An introduction to the Kadison–Singer Problem and the Paving Conjecture [卡迪森 - 辛格問題與鋪砌猜想的介紹] (PDF). 2013-07-11 [2021-10-16]. （原始內容存檔 (PDF) 於 2021-10-21） （英語）.
* 陶哲軒. Real stable polynomials and the Kadison-Singer problem [實穩定多項式與卡迪森 - 辛格問題] (網誌). 2013-11-04 [2021-10-16]. （原始內容存檔於 2022-01-19） （英語）. | [
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超交换作用 | **超交換作用**，或稱克拉默斯 - 安德森（Kramers-Anderson）超交換作用，是離子化合物中一種由非磁性陰離子介導的、近鄰陽離子間的高強度耦合作用。它是同一個陰離子上的兩個電子分別與兩個陽離子彼此耦合的作用結果。相比之下，常見的交換作用只涉及到近鄰金屬離子間的直接耦合。
超交換作用一般是反鐵磁性的，但也有例外。如果兩個陽離子與陰離子共線，則該效應導致反鐵磁性；如果兩個陽離子與介導超交換作用的陰離子間呈 90 度夾角，那麼該效應會變成鐵磁性的相互作用。
超交換作用最早由克拉默斯於 1934 年提出。他意識到在 MnO 晶體中，儘管近鄰的 Mn 離子間存在著非磁性的氧離子，但 Mn 離子之間卻仍然存在磁矩的相互耦合。其後安德森在 1950 年對克拉默斯的模型進行了修正。
1950 年代，古迪納夫和金森順次郎針對超交換作用提出了一系列半經驗公式，現稱作「古迪納夫 - 金森規則」（Goodenough-Kanamori rules）。這一系列規則成功地對一大類材料的磁學特性給出了定性解釋。這些規則是基於電子在重疊的原子軌道中的排布方式和對稱關係而得出的。（這裡的軌道是價鍵理論中的定域軌道，或海特勒 - 倫敦（Heitler-London）模型中的定域軌道。相對於洪特 - 馬利肯 - 布洛赫（Hund-Mulliken-Bloch）模型等離域軌道模型而言，定域軌道模型更適於描述化學鍵。）
泡利不相容原理指出，對於由非磁性離子（如氧離子）介導的兩個陽離子的耦合而言，若兩個陽離子的軌道都是半充滿的，那麼超交換作用將是強反鐵磁性的；若一個陽離子的軌道全充滿，而另一個陽離子的軌道半充滿，則超交換作用是鐵磁性的；若一個陽離子的軌道全充滿 / 半充滿，另一個陽離子帶有空軌道，則耦合既可能是鐵磁性的，也可能是反鐵磁性的，不過多數情況下為鐵磁性。
當多種耦合作用同時存在時，反鐵磁項一般是最強的，因為它與原子內的交換項無關。對於一些簡單的情形，利用古迪納夫 - 金森規則就可以直接預測超交換作用存在時體系的淨磁矩。但在以下幾種情況下，計算可能會更加複雜：
1. 直接交換作用和超交換作用彼此競爭
2. 陽離子 - 陰離子 - 陽離子鍵角不是 180 度
3. 軌道填充狀態不是定態
4. 自旋 - 軌道耦合作用強烈 | [
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超交换作用 | 與超交換作用相關的另一種常見的離子磁矩間耦合作用是雙交換作用。雙交換作用由齊納提出，起先是用於處理電子輸運性質的。它和超交換作用有以下區別：在超交換作用中，參與相互作用的兩個 d 軌道要麼電子數相同，要麼電子數差 2，且涉及的都是定域態電子。而雙交換作用中 d 軌道的電子排布方式不同，且涉及的電子是離域（巡遊）的。因而雙交換作用主導的體系中，材料不僅具有磁序，還具有類金屬的導電性。
## 錳氧化物
以氧化錳為例，在 MnO 中，氧離子的 p 軌道和錳離子的 d 軌道共同參與了超交換作用。
在該系統中，反鐵磁序對應著 d 軌道上的半充滿（單電子填充）態。這種排布方式下，電子離域程度更高，動能更低，因而更穩定。
量子微擾理論中，最近鄰的 Mn 離子對的哈密頓算符為：
$$
{\mathcal {H}}_{1,2}=+{\frac {2t_{\text{Mn,O}}^{2}}{U}}{\hat {S}}_{1}\cdot {\hat {S}}_{2},
$$
式中 $t_{\text{Mn,O}}$ 是 d 軌道與 p 軌道間所謂的躍遷能量， $U$ 則是 Mn 的 Hubbard 能。 ${\hat {S}}_{1}\cdot {\hat {S}}_{2}$ 項是兩個 Mn 離子磁矩矢量間的純量積（海森堡模型）。
結合該哈密頓量，微擾方法給出的結論是近鄰 Mn 離子間的相互作用為反鐵磁性。
## 參考資料
## 外部連結
* Erik Koch. Exchange Mechanisms (PDF). E. Pavarini; E. Koch; F. Anders; M. Jarrell (編). Correlated Electrons: From Models to Materials. Jülich. 2012 [2021-10-20]. ISBN978-3-89336-796-2. （原始內容 (PDF) 存檔於 2022-01-20）. | [
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交换作用 | 在物理學與化學領域中，**交換作用**（以及相關的概念如「交換項」、「交換能」等）是一種僅在全同粒子間出現的量子力學效應。雖然有些地方會將其與經典力學中的力類比而稱之為「交換力」，但它並不是一種真正的力學意義上的相互作用，因為並沒有介導這種相互作用的基本粒子。
該效應是由全同粒子波函數的交換對稱性所引發的。具體的講，互換波函數中的兩個全同粒子後，波函數的概率密度應與交換前完全相同，因而波函數的符號應保持不變（交換對稱）或反號（交換反對稱）。玻色子和費密子都會受到交換作用的影響。對於費密子，交換作用起排斥效果（有時也稱作「泡利排斥」），與泡利不相容原理有關。對於玻色子，交換作用在全同粒子間起等效的吸引作用，與玻色 - 愛因斯坦凝聚有關。在兩個及以上的全同粒子波函數彼此開始重疊時，交換作用將改變它們彼此間距的期望值。與可區分粒子相比，引入交換作用的影響後，費密子的間距期望值增大（即排斥效應），而玻色子的間距期望值減小（即吸引效應）。此外，交換作用最常見的效應是引發磁矩間的耦合，並導致鐵磁性等宏觀磁序。
交換作用是一種純粹的量子力學效應，經典力學中沒有與之對應的概念。該效應在 1926 年由海森堡和狄拉克分別獨立發現。
## 力學描述
交換作用有時也被稱作「交換力」。但它不是一種實際的力，也不應與交換虛粒子所產生的「交換力」相混淆。例如，電子之間通過交換光子而產生電磁力，夸克之間通過交換膠子產生強相互作用力。相對於此而言，交換作用只是一種量子力學「效應」，這與其它的相互作用力有別。
## 定域電子磁矩間的交換作用
量子力學中，粒子依據其自旋可被分為玻色子和費密子。量子場論中的自旋統計定理指出，攜帶半整數自旋的粒子均為費密子，而攜帶整數自旋的粒子均為玻色子。多個全同玻色子可以占據完全相同的量子態，但依據泡利不相容原理，全同費密子不能占據相同的量子態。電子攜帶的自旋為 1/2，是一種費密子，因而材料體系中電子的全體波函數對於任意兩電子的交換操作（包括自旋態和坐標的交換）都是反對稱的。以下先就不考慮自旋的情況下對交換作用進行說明。
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交换作用 | 以包含兩個電子的氫分子系統為例。若要描述該體系中的電子狀態，那麼一種很自然的想法就是先假定兩電子各自獨立運動，並在坐標空間中分別對應波函數 $\Phi _{a}(r_{1})$ 與 $\Phi _{b}(r_{2})$ 。假定兩波函數 $\Phi _{a}$ 與 $\Phi _{b}$ 正交，並各自對應一組能量本徵態，那麼體系中電子的總波函數就可以用兩個電子波函數乘積的反對稱組合來構造（即「反對稱態」）：
:
另一種可行的方式是用對稱組合來構造（即「對稱態」）：
:
這兩種總波函數的構造方式都可以確保交換電子坐標時，波函數將保持不變（ $\Psi _{\rm {S}}$ ）或反號（ $\Psi _{\rm {A}}$ ），即滿足全同粒子不可分辨性的要求。
下面利用微擾法來處理氫分子體系中的交換作用。系統的哈密頓量為：
: ${\mathcal {H}}={\mathcal {H}}^{(0)}+{\mathcal {H}}^{(1)}$
式中 ${\mathcal {H}}^{(0)}=-{\frac {\hbar ^{2}}{2m}}\left(\Delta _{1}+\Delta _{2}\right)-{\frac {e^{2}}{r_{a1}}}-{\frac {e^{2}}{r_{b2}}}$ 為主項，是孤立氫原子哈密頓量之和；第二項 ${\mathcal {H}}^{(1)}=\left({\frac {e^{2}}{R_{ab}}}+{\frac {e^{2}}{r_{12}}}-{\frac {e^{2}}{r_{a2}}}-{\frac {e^{2}}{r_{b1}}}\right)$ 為微擾項，包含質子之間的靜電排斥（_R_ab）、電子之間的靜電排斥（_r_12）和氫分子中額外的質子 - 電子之間的吸引作用（_r_a2/b1）。假設各量值均為實數。
利用微擾法，可解得該系統的兩個能量本徵值：
:
式中 _E_+ 為對稱態對應的能量本徵值，_E_− 為反對稱態對應的能量。變分法給出的結果與微擾法類似。利用式 (1) 和式 (2) 中給出的波函數，可以將 ${\mathcal {H}}$ 對角化。 | [
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交换作用 | 在式 (3) 中，_C_ 是雙勢阱雙電子體系的庫侖積分（可以理解成依 $\Phi _{a}({\vec {r}}_{1})^{2}$ 概率分布的電子在依概率 $\Phi _{b}({\vec {r}}_{2})^{2}$ 分布的另一個電子產生的電場中感受到的排斥勢的積分），_S_ 是重疊積分，_J_ex 一項則是與交換作用相聯繫的「交換積分」，這一項的形式與庫侖積分類似，但其中包含了與電子交換項。這一項沒有與之對應的簡單物理圖像，但從表達式中可以看出，它是在交換反對稱的要求下產生的。這幾個積分項的具體形式為：
:
:
:
儘管氫分子體系中，式 (6) 所示的交換積分是負的，但海森堡指出，隨核間距增大，這一項最終會變號，此時分子軌道退化為單個氫原子的原子軌道。
### 引入自旋
上一節中的公式 (1) 和 (2) 里沒有考慮自旋態的影響。在下列公式中，自旋向上和向下的態分別記作 $\alpha $ 和 $\beta $ 。和波函數的空間坐標部分一樣，自旋部分也有對稱和反對稱的線性組合：
:
將自旋部分添加到式 (1) 和式 (2) 中，即可得到完整的電子波函數。完整的分子軌道波函數可用斯萊特行列式表示。對於電子體系而言，如果軌道空間部分是交換對稱的，那麼自旋部分必須反對稱，反之亦然。和上一節類似，加入自旋後，體系仍有兩個能量本徵值：_E_+ 對應著空間對稱（自旋反對稱）的態（單重態），_E_− 對應著空間反對稱（自旋對稱）的態（三重態）。
范弗雷克在他的教材中進行了如下分析：
>
> 正交軌道中雙電子相互作用的勢能可用一矩陣表出，記作 $E_{\text{ex}}$ 。由式 (3) 可知，該矩陣的特徵值為 $C\pm J_{\text{ex}}$ ，它們正是矩陣對角化後的對角元。 | [
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交换作用 | > 此外，總自旋模長平方 $\langle ({\vec {s}}_{a}+{\vec {s}}_{b})^{2}\rangle $ 的特徵值為 $S(S+1)$ ， $\langle {\vec {s}}_{a}^{\;2}\rangle $ 和 $\langle {\vec {s}}_{b}^{\;2}\rangle $ 的特徵值為 ${\tfrac {1}{2}}({\tfrac {1}{2}}+1)={\tfrac {3}{4}}$ 。三者之間以 $\langle ({\vec {s}}_{a}+{\vec {s}}_{b})^{2}\rangle =\langle {\vec {s}}_{a}^{\;2}\rangle +\langle {\vec {s}}_{b}^{\;2}\rangle +2\langle {\vec {s}}_{a}\cdot {\vec {s}}_{b}\rangle $ 聯繫。由此，純量積 $\langle {\vec {s}}_{a}\cdot {\vec {s}}_{b}\rangle $ 的特徵值即為 ${\tfrac {1}{2}}(0-{\tfrac {6}{4}})=-{\tfrac {3}{4}}$ 和 ${\tfrac {1}{2}}(2-{\tfrac {6}{4}})={\tfrac {1}{4}}$ ，分別對應著自旋單重態（_S_ = 0）與三重態（_S_ = 1）。
>
> 由式 (3) 以及前述關係，當能量 Eex 取得特徵值 _C_ + Jex 時， $\langle {\vec {s}}_{a}\cdot {\vec {s}}_{b}\rangle $ 就會取得特徵值 −3/4（對應著空間對稱態 / 自旋單重態的 S = 0）。而當能量取得特徵值 C − Jex 時， $\langle {\vec {s}}_{a}\cdot {\vec {s}}_{b}\rangle $ 就會取得特徵值 +1/4（對應著空間反對稱態 / 自旋三重態的 S = 1）。因此，
>
>
> :
>
> 也即
>
>
> :
>
> 式中 $\langle {\vec {s}}_{a}\rangle $ 與 $\langle {\vec {s}}_{b}\rangle $ 為自旋角動量項。
>
> | [
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