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解释鸿沟 | 心靈哲學和意識中,**解釋鴻溝**是物理主義者解釋物理性質如何引起感覺經驗的學説。這個屬於由哲學家約瑟夫・萊文發明。 初次使用此術語的 1983 年的論文中,萊文是把這個詞當作例子來用的。「疼痛是 C 纖維的激活」,指出儘管它在心理學意義上可能是有效的,但是它並不幫助我們理解疼痛是什麼感覺。
解釋鴻溝使哲學家既擔心又興奮,類似地,人工智慧研究者幾十年來,也陷入了爭辯。跨越這一鴻溝(即找到一個令人滿意的對經驗和感質的機械論的解釋),也就解決了所謂困難問題。
舉個沒有解釋鴻溝的例子,想像一臺當代的電腦:這些設備非常之先進,他們的行爲也可以得到電路系統的完全解釋。而相反,很多心物二元論者 (例如,勒內・笛卡爾,戴維・查爾莫斯)認爲,「主觀意識經驗」被看作是獨立的結果,所以要求另外一個原因,要麽是物理世界(二元論),要麽是由於未知的物理現象(參見量子心靈,間接實在論)。
二元論的支持者認爲心靈本質上和感質上和大腦不同,還認爲存在一些,形而上的超 - 物理的東西,才能「填滿鴻溝」。相似地,有些人認爲,關於意識經驗存在更遠的事實(邏輯上不由已知物理事實推斷的事實)。例如,有人認爲,經驗到紅色是 什麼感覺和世界的物理事實不同。
解釋鴻溝的本質一直被爭辯。例如,有些人認爲解釋鴻溝簡單地就是我們目前解釋能力的極限。 他們論證道,神經科學未來的發現或者哲學家未來的工作可能會縮小這個鴻溝。但是,也有人支持更強的立場, 論證這個鴻溝是人類認知確切的界限,無論做出什麽努力,都不能讓我們靠近彼岸。 而且,關於鴻溝存在的形上學本質,哲學家也都沒有達成共識。那些希望用它的經驗支持二元論的人,常常會採取知識論鴻溝的立場(尤其如果它是我們人類認知能力的界限的話),必要地,也會牽涉到形上學的鴻溝。
萊文和其他哲學家希望,要麽對物質保持沉默,要麽論證不能得出任何形上學的結論。 萊文同意,構想的能力(指的是哲學殭屍和顛倒光譜論證那種)是建立形上學現實錯誤的方式;但他同時指出,哪怕我們真的在形上學上得出結論,他們仍然會提出闡釋上的問題。
> 儘管我認為唯物主義者的回應最終是正確的,但是想終結心物問題,這在邏輯上還並不充分。哪怕理論最終沒有得出心靈實際上不是物體的結論,或者說心靈性質在形上學上是不可以還原到物理性質的,他們仍然在證明,我們就物理事物而言對心靈事物缺少解釋。
>
> | [
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解释鸿沟 | 但是,這樣的知識論或解釋的問題,可能暗示著一個潛在的形上學問題 —— 感質的非 - 物理性,甚至不能被構想論證證明的東西,都遠沒有被排除在外。
> 最終,我們回到了我們的起點。解釋鴻溝論證並不證明自然原本就存在一個鴻溝,而是我們對自然的理解里存在鴻溝。當然,可能這樣的解釋是合理的:我們對自然的理解的鴻溝,正是自然的鴻溝本身。但是,只要我們有理由質疑後者,我們就需要為前者從別處找些理由。
>
>
根據萊文,問題的核心,是我們缺少理解這個,即完全理解什麼是感質的經驗意味著什麼。他強調,我們不知道,要聞訊這類經驗的本質,什麼範圍是合適的。他用重力定律作爲例子,定律看起來似乎完全解釋了重力,但是卻不能解釋重力常數。類似重力是自然中令人費解的暴力事實,感質也有可能是我們缺少信息或者我們探索不可理解的自然現象的地方。萊文認爲,正如物理或功能狀態的感質經驗可能只是個暴力事實,可能我們應該考慮是不是真的必須要找到一個對感質經驗更徹底的解釋。
萊文指出,關於了解質性經驗知識多少的問題,想解決似乎更加困難,因為我們還缺乏一種方法來闡明,以他心靈中的方式解釋可知的現實是什麽意思。他的確得出結論,我們有充分的理由希望我們對定性經驗做一個更完整的解釋。其中一個非常重要的原因是,意識似乎只在高度組織化的物理系統中展現心靈。當然,這可以表示人類的推理能力不過是組織功能的結果而已。萊文表示,接受這樣的暗示似乎是違反直覺的,因為人類的大腦如此高度組織化,不過它只是例行的執行者。他指出,儘管唯物主義似乎至少具有某種可還原性,但是所有不是物理上不可解釋的東西,其解釋都依賴於可以用物理基礎來描述的機制,這種還原論並不是試圖貶低心理學、物理科學。但是,它仍然需要有包含無法解釋的事實的類別,這些事實與和心理學相關的陳述無關。
## 參見
## 參考資料
## 外部連結
* Joseph Levine's homepage (頁面存檔備份,存於網際網路檔案館)
* _What is it like to be a bat?_ (頁面存檔備份,存於網際網路檔案館) Thomas Nagel, _The Philosophical Review_ LXXXIII, 4 (October 1974): 435-50. | [
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維克托·卡茨 | **維克托・蓋許維奇・卡茨**( **Victor Gershevich (Grigorievich) Kac** ,俄語:Виктор Гершевич (Григорьевич) Кац,1943 年 12 月 19 日生於俄羅斯布古魯斯蘭),美國猶太裔數學家,在蘇聯出生、長大和受教育。
卡茨對數學的興趣始於數學競賽。1960 年,16 歲的他入讀莫斯科國立大學,起初因數學系已滿額,他選擇入讀工程系;後來校方決定為數學系學生加開一班,他才得以進入數學系。卡茨在中學曾學德語,但數學系的入讀要求是懂得基本法語,他自修法語,竟成了同班同學間法語成績最好的一人。1965 年,他進入同校的研究生課程。當時他在本科生第五年後,已經對無限維度的群和無限維度的李代數有所心得 —— 無限維度的李代數以後成了他主要研究對象之一。1968 年他博士畢業;因為他不是莫斯科的永久居民,他求職不順,幸好經過一些數學家的遊說、推薦之下,卡茨當了莫斯科數電學院的教員之一。
1977 年卡茨到了美國(雖然有數學家強烈建議他到以色列發展)。他最初的落腳地是麻省理工學院;他跟這所學校的連繫一直到現今 —— 由初期的訪問助理教授(1977 年)升遷至正教授(1981 年起)。 1981 至 1983 年間他獲斯隆研究獎。
他是美國數學學會院士、莫斯科數學學會榮譽會員、美國文理科學院院士和美國國家科學院會員。
按卡茨的自述,他的研究主要是表示論和數學物理。1967 年,還在蘇聯的卡茨和加拿大數學家羅拔・穆迪在同一年發現了一種無限維度的李代數,以後這個重要結果被稱為卡茨 - 穆迪代數。
卡茨自述他的研究興趣是表示論和數學物理。除了前面提及的李代數和李群,卡茨的研究方向還包括頂點算子代數、量子解析學、可積分系統和表示論。
## 參考
* 維克托・卡茨在麻省理工學院的個人主頁 (頁面存檔備份,存於網際網路檔案館)(英文)
* 生平訪談 (頁面存檔備份,存於網際網路檔案館)(英文)(pdf)
* 美國數學學會院士列表 (頁面存檔備份,存於網際網路檔案館)(英文)
## 外部連結
* Researchgate 上 維克托・卡茨發表的論文及書籍(英文)
* 數學譜系計劃:Victor Gershevich Kac (頁面存檔備份,存於網際網路檔案館)(英文) | [
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] |
維度正規化 | 在量子場論中,**維度正規化**是一種正規化辦法。Giambiagi、Bollini、 傑拉德・特・胡夫特和馬丁紐斯・韋爾特曼都提出了這個辦法。物理學家使用維度正規化來計算費曼圖的積分。積分的值是 d 的亞純函數;d 是時空的維度。
## 其他應用
Wilson–Fisher 固定點、分形維數
## 舉例
: $\int {\frac {d^{d}p}{(2\pi )^{d}}}{\frac {1}{\left(p^{2}+m^{2}\right)^{2}}},$
若 _d_ = 4 − _ε,_上文的積分是
: $\int _{0}^{\infty }{\frac {dp}{(2\pi )^{4-\varepsilon }}}{\frac {2\pi ^{(4-\varepsilon )/2}}{\Gamma \left({\frac {4-\varepsilon }{2}}\right)}}{\frac {p^{3-\varepsilon }}{\left(p^{2}+m^{2}\right)^{2}}}={\frac {2^{\varepsilon -4}\pi ^{{\frac {\varepsilon }{2}}-1}}{\sin \left({\frac {\pi \varepsilon }{2}}\right)\Gamma \left(1-{\frac {\varepsilon }{2}}\right)}}m^{-\varepsilon }={\frac {1}{8\pi ^{2}\varepsilon }}-{\frac {1}{16\pi ^{2}}}\left(\ln {\frac {m^{2}}{4\pi }}+\gamma \right)+{\mathcal {O}}(\varepsilon ).$
有人認為 Ζ 函數正規化和維度正規化是等效的等同因為解析延拓。
## 參考文獻
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維度正規化 | * Bollini, Carlos; Giambiagi, Juan Jose, Dimensional Renormalization: The Number of Dimensions as a Regularizing Parameter., Il Nuovo Cimento B (1971-1996) (Il Nuovo Cimento B), 1972, **12** (1): 20–26 [2020-03-07], doi:10.1007/BF02895558 (不活躍 2020-01-22), (原始內容存檔於 2017-10-16)
* Etingof, Pavel, Note on dimensional regularization, Quantum fields and strings: a course for mathematicians, Vol. 1,(Princeton, NJ, 1996/1997), Providence, R.I.: Amer. Math. Soc.: 597–607, 1999 [2020-03-07], ISBN 978-0-8218-2012-4, MR 1701608, (原始內容存檔於 2019-05-29)
* Hooft, G. 't; Veltman, M., Regularization and renormalization of gauge fields, Nuclear Physics B, 1972, **44** (1): 189–213, Bibcode:1972NuPhB..44..189T, ISSN 0550-3213, doi:10.1016/0550-3213(72)90279-9 | [
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楊代數 | 在表示論中,楊代數(或楊子、**Yangian**)是一種無限維的霍普夫代數和量子群。這是以楊振寧命名的。俄羅斯物理學家弗拉基米爾・德林費爾德和路德維希・法捷耶夫首先研究了楊子。
## 定義
若 a 是半單李代數,Y (a) 是無限維的霍普夫代數(跟泛包絡代數有關係)。Y (a) 是楊代數。
### 有些方程
$$
[t_{ij}^{(p+1)},t_{kl}^{(q)}]-[t_{ij}^{(p)},t_{kl}^{(q+1)}]=-(t_{kj}^{(p)}t_{il}^{(q)}-t_{kj}^{(q)}t_{il}^{(p)}).
$$
若 $t_{ij}^{(-1)}=\delta _{ij}$
$$
T(z)=\sum _{p\geq -1}t_{ij}^{(p)}z^{-p+1}
$$
若 R - 矩陣是 _R_(_z_)= I+ _z_-1 _P_
$$
\displaystyle {R_{12}(z-w)T_{1}(z)T_{2}(w)=T_{2}(w)T_{1}(z)R_{12}(z-w).}
$$
$$
(\Delta \otimes \mathrm {id} )T(z)=T_{12}(z)T_{13}(z),\,\,(\varepsilon \otimes \mathrm {id} )T(z)=I,\,\,(s\otimes \mathrm {id} )T(z)=T(z)^{-1}.
$$
$$
\displaystyle {S(z)=T(z)\sigma T(-z),}
$$
$$
\displaystyle {\sigma (E_{ij})=(-1)^{i+j}E_{2N-j+1,2N-i+1}.}
$$
## 應用
* 楊–巴克斯特方程
* 超對稱楊–米爾斯理論
## 閱讀
* Chari, Vyjayanthi; Andrew Pressley. A Guide to Quantum Groups. Cambridge, U.K.: Cambridge University Press. 1994. ISBN 0-521-55884-0. | [
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楊代數 | * Drinfeld, Vladimir Gershonovich. Алгебры Хопфа и квантовое уравнение Янга-Бакстера [Hopf algebras and the quantum Yang–Baxter equation]. Doklady Akademii Nauk SSSR. 1985, **283** (5): 1060–1064 (俄語).
* Drinfeld, V. G. A new realization of Yangians and of quantum affine algebras. Doklady Akademii Nauk SSSR. 1987, **296** (1): 13–17 (俄語). 翻譯在 Soviet Mathematics - Doklady. 1988, **36** (2): 212–216.
* Drinfeld, V. G. Вырожденные аффинные алгебры Гекке и янгианы [Degenerate affine Hecke algebras and Yangians]. Funktsional'nyi Analiz I Ego Prilozheniya. 1986, **20** (1): 69–70. MR 0831053. Zbl 0599.20049 (俄語). 翻譯在 Drinfeld, V. G. Degenerate affine hecke algebras and Yangians. Functional Analysis and Its Applications. 1986, **20** (1): 58–60. doi:10.1007/BF01077318.
* Molev, Alexander Ivanovich. Yangians and Classical Lie Algebras. Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society. 2007. ISBN 978-0-8218-4374-1. | [
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* Drummond, James; Henn, Johannes; Plefka, Jan. Yangian Symmetry of Scattering Amplitudes in N = 4 super Yang-Mills Theory. Journal of High Energy Physics. 2009, **2009** (5): 046. Bibcode:2009JHEP...05..046D. arXiv:0902.2987 . doi:10.1088/1126-6708/2009/05/046.
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] |
超對稱楊-米爾斯理論 | 在物理學中,**超對稱楊 - 米爾斯** (**SYM**) **理論**跟楊 - 米爾斯理論、弦理論、共形理論、共形對稱、超對稱有關。
## 四維(N=4)
N=4 超楊米理論的拉格朗日量是
: $L=\operatorname {tr} \left\{-{\frac {1}{2g^{2}}}F_{\mu \nu }F^{\mu \nu }+{\frac {\theta _{I}}{8\pi ^{2}}}F_{\mu \nu }{\bar {F}}^{\mu \nu }-i{\overline {\lambda }}^{a}{\overline {\sigma }}^{\mu }D_{\mu }\lambda _{a}-D_{\mu }X^{i}D^{\mu }X^{i}+gC_{i}^{ab}\lambda _{a}[X^{i},\lambda _{b}]+g{\overline {C}}_{iab}{\overline {\lambda }}^{a}[X^{i},{\overline {\lambda }}^{b}]+{\frac {g^{2}}{2}}[X^{i},X^{j}]^{2}\right\},$
$$
F_{\mu \nu }^{k}=\partial _{\mu }A_{\nu }^{k}-\partial _{\nu }A_{\mu }^{k}+f^{klm}A_{\mu }^{l}A_{\nu }^{m}
$$
_i_, _j_ =1,...,6
_a_, _b_ =1,...,4
$f$ 是楊米爾斯規範群的結構常數
$C_{i}^{ab}$ 是 SU (4) 的結構常數
由於非重整化定理,這是一個超共形場論。
## 十維
N=10 的拉氏量是
: $L=\operatorname {tr} \left\{{\frac {1}{g^{2}}}F_{IJ}F^{IJ}-i{\bar {\lambda }}\Gamma ^{I}D_{I}\lambda \right\}+\theta _{I}dCS_{9}^{I}$
I, J = 0, ..., 9
$$
\Gamma ^{I}$ 是 32x32 的矩陣 $(32=2^{10/2})
$$
$\theta _{I}$ 是陳類,CS9 是 9 維的陳 - 西蒙斯形式(陳 - 西蒙斯理論)。
## 應用
* S 對偶的耦合常數: | [
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0.323668509721756,
0.09725944697856903,
0.16903230547904968,
-0.034110188484191895,
0.11135955899953842,
0.4208405017852783,
0.4753757119178772,
0.0021359454840421677,
0.13089215755462646,
-0.4000627100467682,
0.370088666677475,
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] |
超對稱楊-米爾斯理論 | : $\tau ={\frac {\theta }{2\pi }}+{\frac {4\pi i}{g^{2}}}.$
* AdS/CFT 對偶、全像原理、類型 IIB 弦理論、量子引力
* 大 N 展開、平面楊米爾斯理論、 $N^{2-2g}$ 的費曼圖
* Yangian
* 扭量理論、格拉斯曼流形
* 11 維 M 理論、 $N\rightarrow \infty $
## 參考文獻
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汤姆·班克斯 | **托馬斯・湯姆・班克斯** (英語:Thomas Tom Banks,1949 年 4 月 19 日 — ),是羅格斯大學與加州大學聖塔克魯茲分校的理論物理學家和教授,以矩陣理論的奠基者聞名。
## 工作
湯姆・班克斯的研究領域為弦理論及其應用的高能物理學和宇宙學。 他於 1973 年從麻省理工學院取得了他的博士學位。並多次勝任在 普林斯頓高等研究院的訪問學者。
他與威利・費希勒,史蒂芬・申克和 李奧納特・蘇士侃是矩陣理論創始者,試圖以非微擾的方式公理化 M 理論。 此外,班克斯提出的一個猜想稱之為漸近黑暗,認為普朗克尺度上的物理主要是由黑洞所主宰。其目前的研究重心為量子重力、全像原理、以及部分凝態物理領域。
## 引註 | [
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丹尼爾·弗里丹 | **丹尼爾・哈利・弗里丹**(英語:Daniel Harry Friedan,1948 年 10 月 3 日 —)是美國的理論物理學家,在二維量子場論方面有卓越貢獻,同時也是美國女權主義家貝蒂・弗里丹的兒子。他目前是羅格斯大學的教授。
## 傳記
弗里丹於 1980 年在加州大學柏克萊分校取得博士學位,1987 年被任命為麥克阿瑟研究員。1979 年,他指出弦論中的運動方程出自重整化群方程的二維場論。
此外,弗里丹曾在弦理論和凝聚態物理發展出 (1+1) 維系統。其當前研究重心是量子電腦的相關應用。
弗里丹於 2010 年獲頒美國物理協會的拉斯・昂薩格獎。他目前任教於羅格斯大學。
## 個人生活
弗里丹與冰島的一名物理教師 Ragnheiður Guðmundsdóttir 結婚,目前育有兩個女兒及一個兒子。
## 外部連結
* http://www.physics.rutgers.edu/~friedan/(頁面存檔備份,存於網際網路檔案館) | [
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] |
Mermin–Wagner定理 | 在量子場論和統計力學中,**梅爾曼–華格納定理**(**Mermin–Wagner 定理**,或稱**梅爾銘 - 華格納 - 霍亨貝格定理**、**梅爾銘 - 華格納 - 別列津斯基定理**、**科勒曼定理**)闡述了維度 _d_ ≤ 2 的場論沒有自發對稱破缺(要不然無質量的南部玻色子會有無限的相關函數)。
## 概覽
若 φ 是高斯自由場(一種純量場),m 是質量,維度 d=2;傳播子是:
: $G(x)=\left\langle \varphi (x)\varphi (0)\right\rangle =\int {\frac {d^{2}k}{(2\pi )^{2}}}{\frac {e^{ik\cdot x}}{k^{2}+m^{2}}}.$
若 m=0,
: $\nabla ^{2}G=\delta (x).$
因為高斯定律,
: $E={1 \over 2\pi r}.$
: $G(r)={1 \over 2\pi }\log(r)$
若 $r\to 0,\infty $ , $G(r)\to \pm \infty $ ,所以一維或二維的純量場沒有明確定義的平均值。
參見墨西哥帽模型。
## XY 模型的相變
d=2 的 O (2) 模型沒有自發對稱破缺,但是有別列津斯基 - 科斯特利茨 - 索利斯相變。
(量子相變不受影響。)
兩相是:
1、 $G(r)\sim \exp(-r/\xi )$
$$
r/\xi \gg 1
$$
2、冪定律
(_a_ ≪ _r_ ≪ _ξ_
a 是晶格常數
## 海森堡模型
: $H=-J\sum _{\left\langle {i,j}\right\rangle }\mathbf {S} _{i}\cdot \mathbf {S} _{j}.$
## 歷史
## 2D 晶體
## 限制
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物理有机化学 | **物理有機化學**是路易斯・哈米特(Louis Hammett)於 1940 年創造的一個術語,是指關注化學結構與反應性之間關係的有機化學學科,尤其是將物理化學的實驗工具應用於有機分子的研究。研究的重點包括有機反應的速率,原料的相對化學穩定性,反應性中間體,過渡態和化學反應產物,以及非共價方面的溶劑化和影響化學反應性的分子相互作用。 這些研究提供了理論和實際架構,以了解溶液或固態環境中結構的變化如何影響目標有機反應的反應機構和反應速率。
## 應用
物理有機化學家使用理論和實驗方法來理解有機化學中的這些基本問題,包括古典和統計熱力學計算,量子力學理論和計算化學,以及實驗光譜法(例如 NMR),光譜計量法(例如 MS), 和晶體學方法。 因此,該領域可應用於許多更專業的領域,包括電化學和光化學,聚合物和超分子化學,生物有機化學,酶學和化學生物學,以及商業上涉及製程化學,化學工程,材料科學,奈米技術,以及藥理學在藥物發現方面的設計。
## 範圍
物理有機化學是對有機分子的結構與反應性之間關係的研究。 更具體地說,物理有機化學將物理化學的實驗工具應用於有機分子結構的研究,並提供了理論框架來解釋結構如何影響有機反應的機制和速率。 可以將其視為將有機化學與物理化學聯繫起來的子領域。
## 歷史
物理有機化學一詞本身是路易斯・哈米特(Louis Hammett)在 1940 年創造的,當時他將該片語用作教科書的標題。
## 化學結構與熱力學
### 熱化學
有機化學家使用熱力學工具來研究化學系統的鍵結,穩定性和能量學。 這包括測量或確定反應,轉化或異構化的焓(ΔH),熵(ΔS)和吉布斯自由能(ΔG)的實驗。 化學家可以使用各種化學和數學分析(例如 Van't Hoff 圖)來計算這些值。
經驗常數,例如鍵解離能,標準生成熱(ΔH f °)和燃燒熱(ΔH c °)可用來預測分子的穩定性以及反應過程中焓(ΔH)的變化。對於複雜的分子,ΔHf 值可能不可得,但可以使用已知生成熱 (焓) 的分子片段來估算。化學家雪梨・班森(Sidney Benson)窮其職業生涯發展此一概念,通常將這種類型的分析稱為 Benson 群增量理論。
物理有機化學家也對反應性中間體的熱化學反應(碳正離子,碳負離子和自由基)感興趣。 群增量理論可提供自由基系統的資料。碳正離子和碳負離子的穩定性可以分別使用氫化物離子親和力和 pKa 值來評估。
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物理有机化学 | 構形分析是評估化學穩定性和能量學的主要方法之一。 物理有機化學家使用構形分析來評估分子中存在的各種類型的應變,以預測反應產物。在無環和環狀分子中均可發現應變,其在多種系統中表現為扭轉應變,烯丙基應變,環應變和正戊烷應變。A 值為預測被取代的環己烷的構形提供了定量基礎,被取代的環己烷是一類重要的環狀有機化合物,其反應性受構形作用的強烈引導。 A 值是被取代的環己烷的軸向和赤道形式之間的吉布斯自由能之差;藉著將各種取代基的 A 值加在一起,可以定量地預測環己烷衍生物的偏好構形。
除分子穩定性外,構形分析還用於預測反應產物。 通常使用的構形分析方法的一個例子是雙分子消除反應(E2)。 當親核試劑攻擊離去基團反平面的物種時,該反應最容易進行。 對這種現象進行的分子軌道分析顯示,這種構形在經歷親核攻擊的 R-H σ 鍵軌道中的電子與被斷開的 R-X 鍵的空 σ\* 反鍵結軌道之間提供了最佳重疊。利用這種作用,構形分析可用於設計反應性增強的分子。
產生鍵旋轉障礙的物理過程是複雜的,並且已經經由實驗和理論方法對這些障礙進行了廣泛的研究。最近的許多文章研究了在乙烷,丁烷和更多取代的分子中,手性,靜電力和高共軛作用對旋轉障礙的貢獻。
### 非共價交互作用
化學家利用分子內和分子間非共價鍵 / 交互作用的研究來評估反應性。這樣的交互作用包括但不限於氫鍵,帶電分子之間的靜電交互作用,偶極 - 偶極交互作用,極性 -π 和陽離子 -π 交互作用,π- 堆積,供體 - 受體化學和鹵素鍵。此外,疏水作用(水中有機化合物的關聯)是化學家感興趣的靜電、非共價交互作用。疏水作用的精確物理起源來自許多複雜的交互作用,但據信它是水中生物分子識別的最重要組成部分。例如,Xu and Melcher 等闡明了葉酸受體蛋白識別葉酸的結構基礎。葉酸和葉酸受體之間的強交互作用歸因於氫鍵和疏水交互作用。對非共價交互作用的研究還用於研究超分子組裝體和大環化合物(例如冠醚和穴狀配體)中的鍵結和協同作用,這些化合物可以充當客體分子的宿主。
### 酸鹼化學
酸和鹼的性質與物理有機化學有關。 在有機反應中,有機化學家主要關注的是 Brønsted–Lowry 酸 / 鹼作為質子供體 / 受體,以及 Lewis 酸 / 鹼作為電子受體 / 供體。 化學家使用從物理化學發展而來的一系列因素(電負度 / 誘導,鍵強度,共振,混成,芳香性和溶液化)來預測相對酸鹼度。 | [
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] |
物理有机化学 | 硬 / 軟 - 酸 / 鹼原理 (HSAB) 用於預測分子相互作用和反應方向。 通常偏好相同類型分子之間的相互作用。 即,硬酸將與硬鹼結合,而軟酸將與軟鹼結合。 硬酸和硬鹼的概念通常用於合成無機配位化合物。
## 動力學
物理有機化學家使用化學動力學的數學基礎來研究反應速率和反應機制。 與熱力學不同的是,熱力學關注產物和反應物的相對穩定性(ΔG°)及其平衡濃度,動力學的研究重點在於活化的自由能(ΔG‡)–反應物結構之間的自由能差 以及反應的過渡態結構,因此使化學家可以研究平衡過程。數學導出的形式主義,例如哈蒙德推定,科廷 - 漢米特原理和微觀可逆性理論 通常應用於有機化學。 化學家還使用熱力學與動力學控制原理來影響反應產物。
### 速率定律
化學動力學研究用於確定反應的速率規律。 速率定律提供了化學反應速率與存在的化學物質的濃度或壓力之間的定量關係。 速率定律必須通過實驗測量來確定,通常不能從化學方程式中闡明。 實驗確定的速率定律是指過渡態結構相對於基態結構的化學計量。 速率定律的確定,在歷史上是通過重量分析法監測反應過程中反應物的濃度來完成的,但如今,它幾乎只能透過快速,明確的光譜技術來完成。 在大多數情況下,速率方程式的確定透過添加除一種反應物以外過量的反應物(「溢流」)來簡化。
### 催化
催化和催化反應的研究對物理有機化學領域非常重要。催化劑參與了化學反應,但在過程中沒有被消耗。催化劑降低了活化能壘(ΔG・),從而提高了反應速率。原理是經由穩定過渡態結構,或使關鍵的反應中間體不穩定,來進行反應。並且由於僅需要少量催化劑,因此可以經濟地獲得昂貴或難以合成的有機分子。催化劑還可以透過改變反應機制來影響反應速率。
### 動力學同位素效應
儘管速率定律提供了過渡態結構的化學計量,但它不提供有關斷開或形成鍵的任何信息。 接近反應位置的同位素取代通常會導致反應速率發生變化。 同位素取代改變了反應中間體和過渡態的勢能,因為較重的同位素與其他原子形成更強的鍵。 原子質量會影響相關分子的零點振動狀態,在具有較重同位素的分子中鍵長短而牢固,而在具有輕同位素的分子中鍵長較長而弱。 由於在反應過程中振動運動通常會發生變化,此時鍵的形成和斷裂,使得頻率會受到影響,因此利用同位素的取代可以深入了解反應機制和速率定律。
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物理有机化学 | 化學家對取代基如何影響分子的反應性或反應速率的研究非常感興趣。取代基可以透過立體空間及靜電相互作用,以發揮作用,後者包括共振和誘導作用。分子的可極化性也會受到影響。透過線性自由能關係(LFER)可分析大多數取代基的作用。其中最常見的是 Hammett 圖分析。該分析比較了各種取代基對苯甲酸電離的影響以及它們對各種化學系統的影響。 Hammett 圖的參數為 sigma(σ)和 rho(ρ)。 σ 值表示相對於未取代形式的取代苯甲酸的酸度。正的 σ 值表示該化合物的酸性更高,而負的值表示該取代的化合物的酸性更低。 ρ 值用於衡量反應對取代基變化的敏感性,但僅用於衡量感應效應。因此,產生了兩個新的量表,它們通過共振來評估局部電荷的穩定性。一個是 σ+,它表示通過共振穩定正電荷的取代基,另一個是 σ-,它表示通過共振穩定負電荷的基團。哈米特分析可用於幫助闡明反應的可能機制。例如,如果預測到過渡態結構相對於基態結構具有負電荷的積累,則可以預期供電子基團將增加反應速率。
還開發了其他 LFER 量表。通過塔夫脫參數分析立體效應和極性效應。改變溶劑 (而不是反應物) 可以洞悉反應過程中的電荷變化。 Grunwald-Winstein 圖提供了這些效應的定量見解。
### 溶劑效應
溶劑對溶解度、穩定性和反應速率有很大的影響。 溶劑的變化也可以讓化學家影響反應的熱力學或動力學控制。 由於化學轉化過程中電荷分佈的變化,反應在不同溶劑中以不同的速率進行。 溶劑效應可作用於基態和 / 或過渡態結構。 | [
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] |
上海交通大学物理与天文学院 | **上海交通大學物理與天文學院**,前身為上海交通大學物理與天文系,成立於 2017 年。
物理與天文學院最早可追溯於 1906 年的物理實驗室。1928 年成立物理系,1930 年成立科學學院,1952 年院系調整後,物理系停辦,僅留下物理教研室。1978 年重建應用物理系,2001 年改為物理系,2013 年更名為物理與天文系,2017 年更名為物理與天文學院。
物理與天文學院下設交叉科學研究所,凝聚態物理研究所,粒子與核物理研究所,光科學與技術研究所,天文系,雷射電漿體研究所,維爾切克量子中心等九個二級單位、四個省部級重點實驗室、三個基金委創新研究群體、三個教育部創新團隊和兩個科技部創新團隊。
## 參考資料
## 外部連結
* 上海交通大學物理與天文學院 (頁面存檔備份,存於網際網路檔案館) | [
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貝爾態 | **貝爾態**是量子資訊科學中使用到的概念,是兩個量子位元眾多的量子態中的一種,而且是最簡單單純的一種量子糾纏態。貝爾態是一種糾纏並且歸一向量基底的形式。歸一意思是指粒子在該狀態的全域機率是 1: $\langle \Phi |\Phi \rangle =1$ 。糾纏態則是指基底獨立的疊加態.。由於這樣的疊加態,當測量這個量子位元的時候,測量行為會使該量子位元在給定的機率下收斂成基底之一的狀態。然而因為處於糾纏態,測量其中之一的量子位元即等同於馬上給定了另外一個量子位元的測定值,而此測定值會是該貝爾態中給定該量子位元的值。
## 註釋
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玻色新星 | **玻色新星**或**玻色超新星**(Bosenova)是一種極小規模的、類似於超新星的爆炸。這種爆炸可以通過改變玻色愛因斯坦凝聚體(BEC)的外加磁場實現。 由於費什巴赫共振,"自散射" 作用從排斥力變為吸引力導致 BEC「崩潰並反彈」或「震盪」
儘管爆發的總能量非常小,「崩潰並反彈」的描述在性質上很像玻色愛因斯坦凝聚版本的超新星核心坍縮,因此被稱為「玻色新星」。其英文名稱用了巴西音樂流派巴薩諾瓦(Bossa Nova)的梗。
## 實驗
實驗中首次發現玻色新星,是在 BEC 內爆和收縮到小於光學探測器最小解析度時,其自相互作用(Self-interaction)從斥力變為吸引力,並突然「爆炸」。這一爆炸中,凝聚體表面半數的原子似乎「消失」了,也就是說,它們既不存在於剩下的冷粒子中,也不存在於爆炸產生的氣體雲中。
> 幾乎可以肯定,這些「消失」的原子就在附近某處,但並不在我們當前實驗可以探測的形式下。可能的兩種解釋分別是,它們要麼變成了兩個銣原子粘合成的分子,
> 要麼它們已經從某處獲得了足夠的能量,從而以足夠快的速度在我們觀測前飛出我們的視野
>
>
在當前的 BEC 理論中,組成 BEC 的粒子之間的相互作用被計算得十分粗略。這使得玻色新星尚未得到解釋,因為孤立的原子團那幾乎接近絕對為 0 的能量並不足以導致這種觀測到的內爆。不過,一些平均場理論已經嘗試將玻色新星解釋為湧現。
BEC 的玻色新星現象或許可以為中子星的演化研究提供靈感,也可以引導人們猜測尚處在假設階段的玻色子星的可能性質,並促進將量子理論中的集體湧現推廣。
## 參考來源
## 外部連結
* NIST article on the Bosenova phenomenon (頁面存檔備份,存於網際網路檔案館) | [
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中心荷 | **中心荷**是理論物理學中的一個算符_**Z**_,它和其它所有對稱算符都對易。中心意指對稱群的中心,即能與原來的群中所有其它原素對易的元素構成的子群,它通常嵌入在一個李代數中。在一些情況下,如二維共形場論中,中心荷可能和所有其它算符都對易,包括不是對稱性生成元的算符。
## 概述
更精確地說,中心荷是諾特定理中對應於對稱群的中心擴張的中心的荷。
包含超對稱的理論中,這個定義可以推廣到包括超群和李超代數。中心荷可以是與其它超對稱生成元對易的任意算符。擴展了超對稱的理論通常有很多這種算符。在弦論中,第一量子化形式下,這些算符也可解釋為各種弦和膜的卷繞數(拓撲量子數)。
在共形場論中,中心荷是一個 c - 數(與所有其它算符對易)項,出現在應力 - 能量張量的兩個成分的對易子中。
## 參見
* 荷 (物理)
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BB84協定 | **BB84 協定** 是由 Charles Bennett and Gilles Brassard 在 1984 年時所發展出的一種量子密鑰分發方式。它也是第一個量子密碼學協定。 根據量子特性,如果想要鑑別的資訊處於雙態並非正交 (見 不可克隆原理) 且可身分驗證的公開古典通道者,只可能在付出干擾信號本身的代價後,才有可能被取得,因此這個協定是可證安全的。這個協定經常被作為一種安全地從一方傳遞到另外一方來作為一次性密碼本的方法。
## 參考資料 | [
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奈米化學 | **奈米化學**是化學和奈米科學的交叉學科。奈米化學與根據尺寸、表面、形狀和缺陷特性而合成的構件有關。通過進行奈米尺度上的幾種化學修飾,科學家們證實了奈米化學材料具有尺寸依賴性。奈米化學在化學、材料、物理、科學、工程、生物和醫學等領域均有廣泛的應用。奈米化學和其他奈米科學領域的核心概念相同,但這些概念的用法不同。
奈米化學可以由尺寸、形狀、自組裝、缺陷和生物奈米等概念來描述,任何新的奈米結構的合成都與這些概念有關。奈米結構的合成取決於表面、尺寸和形狀將如何引導構件自組裝成功能結構。它們可能存在功能缺陷,也可能在電學、光學、醫學或生物分析等問題上有用。合成碳奈米材料,如碳奈米管(CNT)、石墨烯和富勒烯等,就是一個很好的例子。這些材料因其優異的機械性能和電性能近年來備受關注。
二氧化矽、金、聚二甲基矽氧烷、硒化鎘、氧化鐵和碳等材料都顯示了奈米化學的轉化能力。奈米化學可以將氧化鐵(鐵鏽)製成核磁共振最有效的造影劑,它具有檢測癌症的能力,甚至可以將癌症扼殺在萌芽階段。二氧化矽(玻璃)可以用來彎曲或阻擋光線。開發中國家也用矽膠做流體迴路,以達到已開發國家的病原體檢測能力。碳已經以不同的形狀和形式得到了應用,它將成為電子材料中較好的選擇。
總的來說,奈米化學與化合物的原子結構無關。相反,它涉及的是將材料轉化為解決問題的不同方法。化學主要處理元素週期表中原子的自由度,但是奈米化學帶來了控制材料行為的其他自由度。
## 奈米形貌
奈米形貌是指出現在奈米尺度上的特定表面特徵。在工業上,奈米光刻的應用通常包括電學和人工製造的表面特性。然而,自然界的表面特性也包括在這個定義中,如分子級的細胞相互作用和動物和植物的紋理器官。自然界中的這些奈米形貌特徵具有獨特的用途,有助於調節生物機體的調節和功能,因為奈米形貌特徵在細胞中極為敏感。
## 奈米光刻
奈米光刻是在表面上人工產生奈米形貌蝕刻的過程。許多實際應用都利用了奈米光刻技術,包括計算機中的半導體晶片。奈米光刻技術有很多類型,主要包括:
* 光刻
* 電子束曝光 (EBL)
* X 射線光刻
* 極紫外光刻 (EUVL)
* 光耦合奈米光刻 (LCM)
* 掃描探針顯微鏡 (SPM)
* 奈米壓印光刻
* 浸筆式奈米光刻
* 軟微影技術 | [
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奈米化學 | 每一種奈米光刻技術都有不同的解析度、時間消耗和成本等因素。奈米光刻技術有三種基本方法。一種是使用一種抗蝕材料,這種材料作為 "掩模" 來覆蓋和保護表面上需要光滑的部分。現在可以蝕刻掉未覆蓋的部分,並用保護材料作為模板。第二種方法是直接雕刻所需的圖案。蝕刻可能涉及使用量子粒子束,如電子或光,或化學方法,如氧化或 SAM(自組裝單層)等。第三種方法是將所需的圖案直接放置在表面上,產生最終產品,比原來的表面厚幾奈米。為了使要製作的表面可視化,必須用奈米解析度的顯微鏡對表面進行可視化,這兩種顯微鏡包括掃描探針顯微鏡(SPM)和原子力顯微鏡(AFM)。這兩種顯微鏡也可以參與最終產品的加工。
### 單層自組裝
奈米光刻的方法之一是使用自組裝單層膜(SAM)的方法,該方法為軟方法。SAM 是各種長鏈,可在金表面自組裝,形成有序的單層膜。這種方法的優點是創造一個高質量的結構,其橫向尺寸為 5 奈米到 500 奈米。在這種方法中,通常使用由聚二甲基矽氧烷(PDMS)製成的圖案化彈性體作為掩膜。為了製作 PDMS 印章,第一步是在矽晶片上塗覆一層光致抗蝕劑。下一步是用紫外光曝光該層,然後用顯影劑洗掉曝光的光刻膠。為了降低預聚物的厚度,在圖案母材上用全氟烷基三氯矽烷處理,這些 PDMS 彈性體可用於在平面和曲面上印製微米和亞微米設計化學油墨,以達到不同的目的。
## 應用領域
### 藥物
奈米化學的一個研究較多的應用是醫學。利用奈米化學技術的一種簡單的護膚品就是防曬霜。防曬霜中含有氧化鋅和二氧化鈦的奈米顆粒,這些奈米化學物通過吸收或反射光線,保護皮膚免受有害紫外線的傷害,並通過光激發奈米顆粒中的電子,防止皮膚受到損傷。粒子的激發作用有效地阻斷了皮膚細胞對 DNA 的損傷。
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奈米化學 | 涉及奈米技術方法的新興給藥方法可通過改善身體反應,特異性靶向以及有效的無毒代謝而獲得優勢。許多奈米技術方法和材料可以被功能化用於藥物遞送。理想的材料採用受控激活的奈米材料的奈米材料來攜帶藥物「貨物」進入體內。中孔洞二氧化矽奈米顆粒(Mesoporous silica nanoparticles,MSN)由於其較大的表面積和可進行各種單獨修飾的靈活性,同時在成像技術下顯示出高解析度性能,因此在研究中的應用日益廣泛。不同的奈米級藥物遞送分子的激活方法有很大的差異,但最常用的激活方法是利用特定波長的光來釋放貨物。奈米閥控制的貨物釋放使用低強度的光和電漿體加熱來釋放包含金分子的多種 MSN 的貨物。雙光子激活的光電換能器(2-NPT)使用近紅外波長的光來誘導二硫鍵的斷裂以釋放貨物。近來,由於具有無毒,通過皮膚的自發吸收以及進入血腦屏障的能力,奈米金剛石已顯示出在藥物遞送中的潛力。
#### 生物組織工程
由於細胞對奈米形貌特徵非常敏感,因此組織工程中表面的優化將前沿推向了植入領域。在適當的條件下,利用精心製作的三維支架,引導細胞種子向人工器官生長。三維支架結合了各種奈米級因子,通過控制環境以實現最佳和適當的功能,支架是體外存在、類似於體內細胞外基質的物質,其通過在體外提供必要的複雜生物學因子,可以使人工器官成功生長。其他優點包括細胞表達操縱、粘附和藥物遞送的可能性。
#### 關於傷口
對於擦傷和傷口,奈米化學已證明可以改善癒合過程。電紡絲是一種生物學上用於組織工程的聚合方法,但可以功能化以用於傷口包紮以及藥物遞送。它產生的奈米纖維可以促進細胞增殖, 抗菌性和可控的細胞生長環境,這些特性在宏觀上出現;然而,由於奈米形貌特徵,奈米級版本可能會顯示出更高的效率。 奈米纖維和傷口之間的靶向界面具有更高的表面積相互作用,並且在體內更具有優勢。
有證據表明某些銀奈米顆粒可用於抑制某些病毒和細菌。
奈米化學的新發展提供了各種具有高度可控特性的奈米結構材料。這些奈米結構材料的一些應用包括 SAM 和光刻技術,傳感器中奈米線的使用以及奈米酶。
### 電學
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奈米化學 | 科學家還通過使用汽相和溶液相策略設計了許多具有可控制的長度,直徑,摻雜和表面結構的奈米線組合物。這些取向的單晶被用於半導體奈米線器件中,例如二極體,電晶體,邏輯電路,雷射器和傳感器。由於奈米線具有一維結構,意味著大的表面體積比,因此擴散電阻降低。此外,由於量子限制效應,它們在電子傳輸中的效率使其電學特性易受到輕微擾動的影響,因此,在奈米傳感器元件中使用這些奈米線可以提高電極響應的靈敏度。如上所述,半導體奈米線的一維性和化學柔性使其可應用於奈米雷射中。楊培東和他的同事們對室溫紫外奈米線奈米雷射器進行了一些研究,其中提到了這些奈米雷射器的重要特性。他們得出的結論是,使用短波長奈米雷射在光學計算,信息存儲和微分析等不同領域具有應用。
### 催化劑
#### 奈米酶
奈米結構材料主要用於基於奈米顆粒的酶,由於其顯示出的特殊性質而受到人們的青睞。這些奈米酶的尺寸非常小(1-100 nm),為它們提供了獨特的光學,磁性,電子和催化特性。 此外,對奈米顆粒表面功能的控制以及這些小尺寸酶的可預測奈米結構,使它們在其表面上形成了複雜的結構,從而滿足了特定應用的需求。
### 光伏
奈米化學和奈米材料為低成本的新一代太陽能光伏電池提供了許多機會。奈米粒子表面和結界面的奈米化學界面工程可以增強電荷的分離和收集。最近的研究目標為提高太陽能轉換效率,並降低光伏技術中的器件製造成本。
石墨烯在這個領域因為其特殊的光電性能也受到了重視,最新發表的一篇文獻提出,通過石墨烯摻雜中孔電子選擇層減小光損耗,其具有更好的電氣性能。配合雙端機械堆疊鈣鈦礦 / 矽串聯裝置,通過使介觀的鈣鈦礦頂部電池的背面電極與組織化和金屬化的正面接觸而耦合矽底部電池的接觸,這個光伏電池(有效面積 1.43cm2)表現出 26.3% 的峰值效率,25.9% 的穩定效率。
## 研究
### 奈米金剛石
#### 合成
螢光奈米粒子具有廣泛的應用,但它們在宏觀陣列中的使用使它們能夠有效地應用於電漿體、光子和量子通信,這使它們備受追捧。雖然儘管有很多組裝奈米顆粒陣列的方法,尤其是金奈米顆粒,但它們往往與基底緊密結合,因此不能用濕法化學處理或光刻處理。奈米金剛石允許更大的訪問可變性,隨後可用於耦合電漿體激元波導以實現量子電漿體電路。 | [
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奈米化學 | 奈米金剛石可以通過採用奈米級的碳質晶種來合成,該奈米碳質晶種通過無掩模電子束誘導定位技術通過一步添加胺基團以將奈米金剛石自組裝成陣列,從而一步製備。奈米金剛石表面上的懸空鍵的存在允許它們被各種配位基官能化。這些奈米金剛石的表面被羧酸基團封端,從而通過碳二亞胺偶聯化學使它們與胺端基表面連接。該方法產率較高,並依賴於:在 EDC 存在下,無定形碳和奈米金剛石表面上的胺和羧基官能基之間的鍵合。因此,與金奈米顆粒不同,它們可以承受許多設備應用中的加工和處理。
#### 螢光燈(氮填充)
奈米金剛石的螢光性質源自氮空位(NV)中心的存在,氮原子緊鄰空位。螢光奈米金剛石(FND)於 2005 年發明,此後已用於各種研究領域。該發明於 2008 年獲得美國專利,並在 2012 年獲得了隨後的專利。通過用高能粒子(電子,質子,氦離子)輻照奈米金剛石,然後在 600–800°C 下進行真空退火,可以創建 NV 中心。輻照會在鑽石結構中形成疫苗,而真空退火會將這些空位遷移,這些空位將被奈米金剛石中的氮原子捕獲。此過程產生兩種類型的 NV 中心。形成了兩種類型的 NV 中心 —— 中性(NV0)和帶負電(NV–),它們具有不同的發射光譜。 NV - 中心特別受關注,因為它具有 S = 1 的自旋基態,可以通過光泵浦將其自旋極化,並使用電子順磁共振對其進行操縱。螢光奈米金剛石結合了半導體量子點(小尺寸,高光穩定性,明亮的多色螢光)與生物相容性,無毒和豐富的表面化學的優點,這意味著它們具有革新體內成像應用的潛力。
#### 藥物遞送和生物相容性
奈米金剛石具有自組裝的能力,並且各種各樣的小分子,蛋白質抗體,治療劑和核酸都可以與其表面結合,因此其可以進行藥物遞送,模擬蛋白質和外科手術植入物。其他潛在的生物醫學應用是將奈米金剛石用作固相肽合成的載體,並用作解毒和分離的吸附劑;以及將螢光奈米金剛石用於生物醫學成像。奈米金剛石具有生物相容性,具備多種可用於治療的能力,包括:在水中的分散性和可擴展性,以及靶向療法潛在的藥物輸送平台所需的所有特性。奈米金剛石的小尺寸,穩定的核,豐富的表面化學,自組裝能力和低細胞毒性讓人們提出可以將它用於模擬球狀蛋白。奈米金剛石用於一般藥物遞送的潛在可注射治療劑的應用已被大量研究,但也已表明,聚對二甲苯奈米金剛石複合材料的薄膜可用於在兩天至一個月的時間內局部持續釋放藥物。
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奈米化學 | 奈米級單雜散團簇(也稱為奈米團簇)是合成生長的晶體,其大小和結構會通過勢阱影響其性能。合成這些奈米簇卻是一個難題。一種生長這些晶體的方法是在非水性溶劑中通過反膠束籠。對 MoS2 奈米團簇的光學性質進行的研究將它們與大塊晶體對應物進行了比較,並分析了它們的吸收光譜。分析表明,塊狀晶體對吸收光譜的尺寸依賴性是連續的,而奈米團簇的吸收光譜具有離散的能階。這表明在報告的簇大小為 4.5 – 3.0 nm 時發生了從固體到分子的轉變。
由於它們在磁記錄,磁流體,永磁體和催化方面具有潛在用途,人們對奈米團簇的磁性感興趣。對鐵團簇的分析表明,由於團簇內部存在強磁性相互作用,其行為與鐵磁和超順磁的行為一致。
奈米團簇的介電性質也是一個研究主題,因為它們在催化,光催化,微電容器,微電子學和非線性光學中有可能被應用。
### 著名的研究人員
在奈米化學領域,有幾位研究人員對該領域的發展做出了卓越貢獻,來自多倫多大學的 Geoffrey A. Ozin 就是其中一例。他在這一領域的研究長達 45 年,被稱為 "奈米化學的奠基人之一"。其研究包括矩陣隔離雷射拉曼光譜,裸金屬團簇化學、光化學,奈米多孔材料,混成奈米材料,介觀材料和超薄無機奈米線。
另一位被視為奈米化學先驅之一的化學家是哈佛大學的查爾斯・利伯。他以其在奈米技術發展方面的貢獻而著稱,特別是在生物學和醫學領域的貢獻。這些技術包括奈米線,這是一類新的准一維材料,表現出優異的電、光、機械和熱性能,有可能被用作生物傳感器。Lieber 領導的課題組已經深入研究了奈米線用於繪製大腦活動圖譜的課題。
加州大學洛杉磯分校教授西蒙・魏斯(Shimon Weiss)以研究螢光半導體奈米晶體(量子點的一個子類)用於生物標記的研究而聞名。來自加州大學伯克利分校的保羅・阿利維薩托斯在奈米晶體的製造和使用方面的研究也很有名。這項研究潛力較大,會對小尺度粒子的成核、陽離子交換和分支過程等小尺度粒子的機理進行深入研究。這些晶體的一個值得注意的應用是量子點的開發。
另一位來自加州大學伯克利分校的楊培東研究員也因其在一維奈米結構的發展上的貢獻而引人注目。目前,楊培東課題組在奈米線光子學、基於奈米線的太陽能電池、用於太陽能轉化為燃料的奈米線、奈米線熱電學、奈米線 - 電池界面、奈米晶體催化、奈米管奈米流體學、電漿體等領域都有活躍的研究項目。
## 生產安全
: 詳情參見:奈米材料 - 健康與安全
## 備註
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奈米化學 | ## 精選書籍
* J.W. Steed, D.R. Turner, K. Wallace _Core Concepts in Supramolecular Chemistry and Nanochemistry_ (Wiley, 2007) 315p. ISBN 978-0-470-85867-7
* Brechignac C., Houdy P., Lahmani M. (Eds.) _Nanomaterials and Nanochemistry_ (Springer, 2007) 748p. ISBN 978-3-540-72993-8
* H. Watarai, N. Teramae, T. Sawada _Interfacial Nanochemistry: Molecular Science and Engineering at Liquid-Liquid Interfaces_ (Nanostructure Science and Technology) 2005. 321p. ISBN 978-0-387-27541-3
* Ozin G., Arsenault A.C., Cademartiri L. _Nanochemistry: A Chemical Approach to Nanomaterials_ (頁面存檔備份,存於網際網路檔案館) 2nd Eds. (英國皇家化學學會,2008) 820p. ISBN 978-1847558954
* Kenneth J. Klabunde; Ryan M. Richards (編). 化学中的纳米材料 2nd. Wiley. 2009. ISBN 978-0-470-22270-6. | [
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三重态氧 | **三線態氧**, _3_O2,指的是雙原子氧( ${\ce {O2}}$ )的 _S_ = 1 電子基態。它是最常見、最穩定的氧的同素異形體。三線態氧分子包含兩個不成對的電子,這使三線態氧成為穩定且經常遇到的不尋常的例子雙自由基。根據分子軌道理論,三線態氧的電子構型有兩個電子,它們占據了兩個等能量的 π 分子軌道 (MOs)(即簡併的 MOs)。根據洪德規則,它們保持電子對並且自旋平行,並占分子氧的順磁性。這些半填充的軌道具有反鍵軌道特徵,將分子的總鍵序從最大值 3(例如,二氮)降低到 2,這在這些反鍵軌道保持完全未被占用時發生。 三線態氧的分子符號是 3Σ−
g。
## 自旋
簡併軌道中兩個電子的 _s_ = 1⁄2 自旋,總共產生 2 × 2 = 4 個獨立的自旋態。交換相互作用將其分為單重態(總自旋 _S_= 0)和一組 3 個簡併三線態 (_S_= 1)。與洪德規則一致,三線態在能量上更有利,並且對應於分子的基態,總電子自旋為 _S_= 1。激發到 _S_ = 0 會產生更多反應性亞穩態單重態氧
### 路易斯結構
因為處於基態的分子具有非零的自旋磁矩,所以氧為順磁性; 即,它可以被吸引到磁鐵的兩極。因此,具有全部成對的電子的路易斯結構 O=O 不能精確地表示分子氧中鍵的性質。但是,・O–O・的替代結構也不夠用,因為它暗示了單鍵的特性,而實驗確定的為 121 pm 的鍵長比過氧化氫 (HO–OH) 中 147.5 pm 的單鍵短得多。這表明三線態氧具有更高的鍵序。 必須使用分子軌道理論來正確解釋同時觀察到的順磁性和短鍵長。在分子軌道理論的框架下,三線態雙氧中的氧 - 氧鍵更好地描述為一個完整的 σ 鍵加上兩個 π 半鍵,每個半鍵均由兩中心三電子(2c-3e)鍵構成,給出兩個淨鍵合順序(1+2×1/2),同時還要考慮自旋狀態(_S_ = 1)。在三線態雙氧的情況下,每個 2c-3e 鍵由 πu 鍵合軌道中的兩個電子和 πg 反鍵合軌道中的一個電子組成,以提供 1/2 的淨鍵階貢獻。
必須修改構造路易斯結構的常規規則,以適應包含 2c-3e 鍵的三線態雙氧或一氧化氮之類的分子。 在這方面尚無共識; 鮑林建議使用三個緊密間隔的共線點來表示三電子鍵(參見插圖)。
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三重态氧 | 觀察雙氧順磁性的常用實驗方法是將其冷卻至液相。 當倒在彼此靠近的強磁體的磁極之間時,液態氧可以懸浮。 或者,磁鐵可以在倒入液氧時拉動液氧流。 分子軌道理論為這些觀察提供了解釋。
## 反應
不尋常的電子結構阻止了分子氧直接與許多其他處於單重態的分子直接反應。 但是,三線態氧將很容易與處於雙重態的分子反應形成新的自由基。
在三線態氧與閉殼(單重態分子)的反應中,自旋量子數的守恆將需要三線態過渡態。 所需的額外能量足以防止在環境溫度下與反應性最強的底物(例如活性炭)以外的所有底物直接反應。 白磷。 在較高溫度下或在合適的催化劑存在下,反應更容易進行。 例如,大多數易燃物質的特徵是自燃溫度,在這種溫度下,它們將在空氣中燃燒而沒有外部火焰或火花。
## 參考文獻
## 擴展閱讀
* 國際純化學和應用化學聯合會,_化學術語概略_,第二版。(金皮書)(1997)。在線校正版: (2006–) "singlet molecular oxygen (singlet molecular dioxygen)"。doi:10.1351/goldbook.S05695
## 外部連結
* http://meta-synthesis.com/webbook/16\_diradical/diradical.html(頁面存檔備份,存於網際網路檔案館) | [
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芯片级原子钟 | **晶片級原子鐘**(英語:Chip-scale atomic clock,縮寫为 CSAC)是使用微機電系統(MEMS)技術製造的緊湊型低功耗原子鐘,並結合了低功耗半導體雷射器作為光源。基於 2001 年的一項發明,2003 年在國家標準技術研究所上展示了第一個晶片級原子鐘物理軟體包。這項工作是由美國國防部國防高級研究計劃局(DARPA)資助的,目的是開發一種微晶片大小的原子鐘,用於可攜式設備。在軍事裝備中,當全球定位系統不可用時,有望為下崗士兵提供更好的位置和戰場態勢感知,但也可以設想許多民用應用。這些原子鐘的商業生產始於 2011 年。晶片級原子鐘是世界上最小的原子鐘,其尺寸為 4 x 3.5 x 1 厘米(1.5 x 1.4 x 0.4 英寸),重 35 克,僅消耗 115 毫瓦的功率,也可以在運行幾年後將時間保持在每天 100 微秒以內。
## 原理
像其他銫原子鐘一樣,該時鐘通過銫 133 原子中兩個超精細能級之間的電子自旋躍遷發射的精確的 9.192631770 吉赫茲微波信號來保持時間。反饋機制將晶片上的石英晶體振盪器鎖定在該頻率,該頻率被數字計數器分頻,以提供 10 兆赫茲和 1 赫茲的時鐘信號提供給輸出引腳。在晶片上,使用矽微機械加工技術製造的 2 毫米微型膠囊中的液態金屬銫被加熱以蒸發鹼金屬。半導體雷射器將微波振盪器調製的紅外光束通過膠囊照射到光電探測器上。當振盪器處於躍遷的精確頻率時,銫原子的光吸收會減少,從而增加了光電探測器的輸出。光電檢測器的輸出在鎖頻環電路中用作反饋,以將振盪器保持在正確的頻率。
## 發展歷程 | [
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芯片级原子钟 | 常規的蒸氣室原子鐘大約是一副紙牌的大小,消耗約 10 瓦的電能,成本約為 3,000 美元。 將這些縮小到半導體晶片的大小需要大量的開發和一些突破。開發的重要部分是設計該設備,以便在可能的情況下使用標準的半導體製造技術製造該設備,以使其成本保持足夠低的水平,從而使其可以成為大眾市場的設備。常規銫鐘使用裝有銫的玻璃管,要使其直徑小於 1 厘米是很困難的。在晶片級原子鐘中,使用 MEMS 技術製造了尺寸僅為 2 立方毫米的銫膠囊。常規原子鐘中的光源是銣氣體放電燈,其體積龐大且消耗大量功率。在晶片級原子鐘中,這由在晶片上製造的垂直腔面發射雷射器(VCSEL)代替,其光束向上輻射到其上方的銫囊中。另一個進步是消除了傳統時鐘中使用的微波腔,該微波腔的大小等於微波頻率的波長(約 3 厘米),構成了時鐘大小的基本下限。通過使用量子技術,相干的人口陷阱,空腔變得不必要。
## 商業化
至少有一個公司 Microsemi 生產這種時鐘的版本。
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干涉仪类型列表 | ## 現場和線性干涉儀
* 氣楔式剪切干涉儀
* 天文干涉儀 / 麥可遜恆星干涉儀
* 經典干涉顯微鏡
* 共同的道路 - 浴
* 循環干涉儀
* 衍射光柵干涉儀 (白光)
* 雙縫干涉儀
* 雙極化干涉儀
* Fabry–Pérot 干涉儀
* 菲索干涉儀
* 傅立葉變換干涉儀
* 菲涅耳干涉儀 (例如 菲涅 耳雙稜鏡 , 菲涅耳鏡或勞埃德鏡 )
* 等色階干涉儀(FECO)的邊緣
* 伽柏全息圖
* Gires–Tournois 標準具
* 外差式干涉儀 (請參閱外差 )
* 全息干涉儀
* 賈明干涉儀
* 雷射都卜勒振動計
* Linnik 干涉儀 (顯微鏡)
* 麥可遜的 LUPI 變體
* Lummer-Gehrcke 干涉儀
* 馬赫曾德爾干涉儀
* 馬丁・普普特干涉儀
* 麥可遜干涉儀
* Mirau 干涉儀 (也稱為 Mirau 物鏡)(顯微鏡)
* 莫爾干涉儀 (請參見莫爾圖案 )
* 多光束干涉儀 ( 顯微鏡 )
* 近場干涉儀
* 牛頓干涉儀 (請參閱牛頓環 )
* 諾瑪斯基幹涉儀
* 非線性麥可遜干涉儀 / 階躍式麥可遜干涉儀
* N 縫干涉儀
* 移相干涉儀
* 平面光波電路干涉儀 (PLC)
* 光子都卜勒測速儀干涉儀 (PDV)
* 偏振干涉儀 (另請參見 Babinet–Soleil 補償器 )
* 點衍射干涉儀
* 瑞利干涉儀
* Sagnac 干涉儀
* Schlieren 干涉儀 (相移)
* 剪切干涉儀 (橫向和徑向)
* Twyman–Green 干涉儀
* Talbot–Lau 干涉儀
* 沃森干涉儀 (顯微鏡)
* 白光干涉儀 (另請參閱光學相干斷層掃描 )
* 白光散射板干涉儀 (白光)(顯微鏡)
* 楊氏雙縫干涉儀
* Zernike 相襯顯微鏡
## 強度和非線性干涉儀
* 強度干涉儀
* 強度光學相關器
* 頻率分辨光學選通 (FROG)
* 頻譜相位干涉法用於直接電場重建 (SPIDER)
## 量子光學干涉儀
* Hong-Ou-Mandel 干涉儀 (HOM)(請參閱 Hong-Ou-Mandel 效應 )
* 弗蘭森干涉儀
* 漢伯里 - 布朗特維斯干涉儀
* 極化子干涉儀
## 光學外部干涉儀
* 聲干涉儀
* 原子干涉儀
* 中子干涉儀
* 拉姆西干涉儀
* 迷你聖杯乾涉儀
* Aharonov–Bohm 效應
* 干涉式合成孔徑雷達 (基於雷達的 3-d 表面映射) | [
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] |
干涉仪类型列表 | * 超導量子干涉儀(SQUID)
* White–Juday 扭曲場干涉儀
## 參看
* 阿塔卡馬大型毫米波陣列 | [
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龍愛量子 | **龍愛量子**,是中國大陸一個傳銷組織,成立於 2016 年 11 月。公司開發以「量子技術」冠名的產品,並宣稱其產品有奇效,藉此吸納群眾投資。2017 年 7 月,龍愛量子被警方查封,查封時有逾 125 萬名投資人,涉案資金逾 9 億人民幣。
2016 年 6 月,林躍慶在廣東省東莞市以銷售量子高科技產品為名,之後便購買產品、發展下線、繳納會費的方式,以高額動態、靜態收益為誘餌,在網際網路上吸引參加者並按一定的順序組成層級開展傳銷活動。根據龍愛量子的官方網站介紹,其提供墨子號衛星的動力系統和通信系統,亦取得 43 項的國家專利。龍愛量子亦稱其得到國家立法認可,產品和技術三十年內全球沒有競爭對手。2017 年 7 月,龍愛量子被警方查封,查封時有逾 125 萬名投資人,涉案資金逾 9 億人民幣,隨後各地法院陸續對參與龍愛量子的人員判刑。
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艾雪·佩雷斯 | **艾雪・佩雷斯**(希伯來語:אשר פרס 1934 年 1 月 30 日 —2005 年 1 月 1 日)以色列物理學家,生於法國多爾多涅河畔博略,量子信息和量子力學與相對論關係領域先驅,曾提出哈密頓 - 雅可比 - 愛因斯坦方程,博士導師為以色列理工學院納森・羅森。 | [
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] |
石墨炔 | **石墨炔**(Graphyne)是碳的同素異形體。它是由單原子厚的,sp 雜化和 sp2 雜化的碳原子構成的晶體。它可以看成用碳碳三鍵連接而成的苯。根據鍵的種類,石墨炔中的碳可以看作是混合的 spn 雜化,1<n<2。因此它與石墨(sp2)和鑽石(sp3)均有所不同。
石墨炔在 1960 年代就已被推測存在,並且在富勒烯被發現後獲得了相當的關注。
儘管當時並未合成,但石墨炔和它的氮化硼同構體的周期性結構在藉助聲子色散曲線、從頭計算法計算的有限溫度和量子分子動力學模擬的第一性原理的計算下被證明是穩定的。
## 結構
目前石墨炔尚未有足以進行研究的製備產出,但科學家在推測的晶格結構之上通過計算機建模預言了這種化合物的諸多性質。這種可能的結構是在把石墨烯晶格中的碳碳單鍵替換成三鍵後得到的。理論上石墨炔可能存在數種不同的幾何結構,這種不同來源於碳原子的 sp 雜化和 sp2 雜化的不同排列。推測的幾何結構包括六方晶系和立方晶系。有人認為石墨炔中可能存在的方向相關的狄拉克錐使它在一些方面較石墨烯更有應用前景。在多種理論推導出的結構中立方晶系的 6,6,12 - 石墨炔似乎有著最好的應用前景。
## 性質
石墨炔的模型表明在碳碳雙鍵和三鍵上可能有狄拉克錐存在。狄拉克錐會使得費米能級中存在一個導帶和價帶線性相交的點。這種性質的優點是電子在其中會表現得沒有質量,結果使電子能量與動量成正比。與石墨烯一樣六方晶系的石墨炔有著各向同性的電磁屬性。但是由於立方晶系 6,6,12 - 石墨炔的對稱性,它的電磁屬性會在各個方向有所不同。這種獨特的對稱屬性使得石墨炔可以自摻雜,使它擁有兩個分別在費米能級上下,距離不遠的狄拉克錐。在面內施加外應變可以調節 6,6,12 - 石墨炔的這種自摻雜特性。新近合成的石墨炔樣品的熔點在 250 至 300°C,與氧反應,在熱,光下分解均不活躍。
## 潛在應用
6,6,12 - 石墨炔的方向選擇性使奈米尺度的電子光柵成為可能。它還可能會為更快的電晶體和奈米尺度電子元件帶來巨大的進展。
## 石墨二炔
現有報導中石墨二炔的製備是在銅表面上得到的 1mm 厚的薄層。石墨二炔可能會有一種奈米尺度的三角形網狀結構和規則分布的孔,從而構成奈米多孔膜。這些毛孔的尺寸和氦原子范德華半徑相近,因此石墨二炔可能會成為適合氦化學和同位素分離的二維材料。石墨二炔膜作為二維篩應用於水過濾和淨化技術的可能性亦被提出。 .
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海因里希·鲁本斯 | **海因里希・魯本斯**(Heinrich Rubens,(1865 年 3 月 30 日 —1922 年 7 月 17 日)) 是一名德國物理學家。
## 生平
1865 年生於拿騷公國威斯巴登的一個猶太家庭。在美因河畔法蘭克福上完高中後,1884 年起,他在達姆施塔特和柏林的技術大學學習電氣工程 。第二年,轉至柏林大學學習物理學 。一學期後,轉至斯特拉斯堡。1888 年,魯本斯獲得了博士學位。1890-1896 年間,被聘為物理研究所的助理,並在 1892 年取得特許任教資格。當時他已因為對紅外線(infrared radiation)的實驗性研究而受到讚揚。
1896 年,魯本斯在柏林夏洛滕堡的柏林工業大學獲得了一份講師職位。使得他可以在德國聯邦物理技術研究院附近繼續他的實驗研究。1900 年,他在那裡完成了對黑體輻射(black-body radiation)的重要測量,而聞名於世。同年被提升為教授。
1906 年,保羅・德魯德從柏林大學的教授職位離任。魯本斯獲得了這個職位,並被任命為物理研究所所長。1908 年,入選普魯士科學院。1910 年獲得拉姆福德獎章後參加了第一屆索爾維會議。
1922 年,因長期患病去世。
## 後事
馬克斯・普朗克(Max Planck)在一次科學院的紀念會議上,談到魯本斯:
「Without the intervention of Rubens the formulation of the radiation law and thereby the foundation of quantum theory would perhaps have arisen in quite a different manner, or perhaps not have developed in Germany at all.」
魯本斯的黑體輻射研究,影響了普朗克的研究,推動了量子力學的發展。
## 家庭
* 妻、瑪麗,1941 年因害怕遭納粹驅逐和殺害而自殺 。
## 成就
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] |
张东才 | **張東才**(英文名:Donald C. Chang,1942 年 —)是香港科技大學的一位創校教授。他還是香港生物物理學會的創始會長。他目前是香港科大的榮休教授和兼職教授,以及香港科學會(HKIS)的理事會成員。他的研究涉及核磁共振、生物物理學,以及量子物理學。
## 核磁共振在檢測癌症上的應用
張東才是應用核磁共振(spin-echo NMR)技術研究細胞中水的物理性質的先驅。張在萊斯大學物理系工作時,製作了 NMR 光譜儀來測量和分析純水、正常細胞(或細胞組織)中水與癌症細胞中的水的不同物理特性,主要是測量這些不同狀態水的兩種弛豫時間(relaxation time):T1 和 T2。通過對比這三種情況下的水的不同狀態,張和其合作者在 1971 年首次報告發現正常細胞中的水的弛豫時間比純水的弛豫時間要短得多。
1972 年,他的團隊使用相同的技術測試乳腺組織中的正常細胞和癌細胞的弛豫時間。發現從正常細胞發展到腫瘤前細胞,再到腫瘤細胞,其細胞中水的弛豫時間會依次增加。這一發現意味著利用核磁共振技術(NMR)可以檢測出癌前細胞和癌細胞。
## 電穿孔和電融合技術
1980 年代初期,研究人員發現,可以使用強電脈衝使細胞膜變得可以瞬時滲透。在細胞膜「打開」的瞬間,許多大分子物質,包括 DNA、RNA 和一些蛋白質都可以通過這些細胞膜上的洞進入細胞。一段時間後,細胞膜上的洞會關閉,細胞膜會復原。這種技術被稱為「電穿孔」(Electroporation)。
張的團隊發明了一種利用脈衝射頻電場實現電穿孔的技術,該技術使得對細胞進行基因轉染和細胞融合的效率得到巨大提升。(「電融合」(electrofusion)使用與電穿孔大致相同的技術,不同之處在於電融合涉及兩個細胞的融合)。
## 量子物理學
根據麥克斯韋理論,張研究了普朗克常數的物理意義。普朗克常數 _h_ 是最重要的通用常數之一。但是,_h_ 的物理性質尚未被很好地理解。普朗克關係最初是基於解釋觀察到的現象而提出的,而不是基於第一原理推導而成的。張的文章表明,通過將光子建模為電磁輻射的波包,可以根據麥克斯韋理論直接計算能量和動量。他使用光子的發射和傳播都遵循了「全或無」(all-or-none)的原理。他發現波包的能量與其振盪頻率成正比。這樣就可以直接導出普朗克常數。這表明普朗克常數與真空的物理性質密切相關。
## 參考文獻 | [
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] |
Z-矩阵 | 在化學中,**Z - 矩陣**(英語:Z-matrix)是表示由原子構成的系統的一種方式。 Z 矩陣有時也被稱為內坐標(英語:internal coordinate representation)。
## 性質
Z - 矩陣提供了分子中每個原子的原子序數,鍵長,鍵角和二面角(即所謂的內部坐標)的描述。然而 Z - 矩陣並非總能提供化學鍵相關的信息,因為矩陣本身是基於描述空間中原子取向的一系列向量的。但是 Z - 矩陣仍是一種對鍵長,鍵角和二面角等性質的方便表示,畢竟它能保留實際的鍵連關係。Z - 矩陣這個名字來源於生成 Z - 矩陣時將第一個原子與第二個原子的連線設為 Z 軸這一規則。
Z - 矩陣可以與笛卡爾坐標系相互轉換,但是空間中的位置和方向卻不同。儘管從概念上講轉換是簡單易懂的,但是進行轉換的算法在速度,數值精度和並行度上卻有很大差異。這一點很重要,因為高分子鏈(例如聚合物,蛋白質和 DNA)可以具有成千上萬個相連的原子,並且沿該鏈連續相距很遠,這些原子在笛卡爾空間中可能很近(因此,較小的捨入誤差可能會累積成不可忽視的力場誤差)從扭轉空間到笛卡爾空間轉換的最佳最快和最精確的數字算法是自然擴展參考系方法。從笛卡爾角到扭轉角的反向轉換是簡單的三角函數,並且沒有累積誤差的風險。
## 應用
在許多分子建模和計算化學程序中,Z - 矩陣用於為分子系統創建輸入文件。熟練選擇內部坐標可以使結果的解釋簡單明了。另外,由於 Z 矩陣包含的分子連接性信息(雖然並不總是包含此信息)可以用於更有根據地猜測初始的黑塞矩陣,一些量子化學計算(比如結構優化)可以因此而加快速度。目前,Z 矩陣通常是首選的分子表示法,因為這可以通過將某些角度設置為常數來對分子(或其部分)強制添加對稱性。 Z 矩陣只是以相對方式放置原子位置的一種表示形式,具有明顯的便利性,即 Z 矩陣中使用的向量對應於化學鍵。一個概念上的陷阱是假設所有鍵在 Z 矩陣中都顯示為一條線,這是不正確的。例如:在像苯這樣的環狀分子中,Z 矩陣將不會包含環中的所有六個鍵,因為所有六個原子的位置僅在記錄 5 個鍵之後就唯一確定,從而使第 6 個多餘。
## 例子
以下是一個甲烷分子的笛卡爾坐標表示
```
C 0.000000 0.000000 0.000000
H 0.000000 0.000000 1.089000 | [
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] |
Z-矩阵 | H 1.026719 0.000000 -0.363000
H -0.513360 -0.889165 -0.363000
H -0.513360 0.889165 -0.363000
```
我們把坐標軸稍微旋轉,可以得到如下對稱性更明顯的坐標
```
C 0.000000 0.000000 0.000000
H 0.628736 0.628736 0.628736
H -0.628736 -0.628736 0.628736
H -0.628736 0.628736 -0.628736
H 0.628736 -0.628736 -0.628736
```
進而,以碳原子為原點,我們可以構建如下 Z - 矩陣
```
C
H 1 1.089000
H 1 1.089000 2 109.4710
H 1 1.089000 2 109.4710 3 120.0000
H 1 1.089000 2 109.4710 3 -120.0000
```
其中 H 1 1.089000 表示此 H 原子離第一個原子的距離為 1.089000, H 1 1.089000 2 109.4710 表示此 H 原子離第一個原子的距離為 1.089000 且與 1,2 號原子所成鍵角為 109.4710 度,H 1 1.089000 2 109.4710 3 120.0000 表示此 H 原子離第一個原子的距離為 1.089000 且與 1,2 號原子所成鍵角為 109.4710 度,且與 1,2,3 號原子所成二面角為 120 度。
## 引用 | [
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Davis-Kahan定理 | **Davis-Kahan 定理(Davis-Kahan theorem)** 是隨機矩陣分析中的一個重要的基礎性定理。它的基本內容是,如果兩個矩陣在某種合適的模之下相近,且有足夠的特徵裂隙,那麼它們相應的特徵向量子空間也相似。
## 定理內容
### 兩個線性空間的夾角
考慮兩個單位列正交矩陣 $V,{\hat {V}}\in \mathbb {R} ^{n\times d}$ (「單位列正交」意為:其滿足 $V^{T}V={\hat {V}}^{T}{\hat {V}}=I_{d}$ ) 之列向量分別張成的線性子空間,那麼這兩個子空間的張角,是由一個矩陣所表示的(顯然這是如下熟知的特殊情形之概念上的拓展: $d=1$ 時,通常用一個數值表示兩個向量之間的張角),式子如下:
: $\Theta (V,{\hat {V}})=\mathrm {Diagonal} (\arccos \langle V_{\cdot 1},{\hat {V}}_{\cdot 1}\rangle ,\ldots ,\arccos \langle V_{\cdot d},{\hat {V}}_{\cdot d}\rangle )$
上式中,「 $\Theta $ 」是一個數學運算,表示線性空間之間的張角。
### 定理的經典版本
有了線性空間之間張角的定義,便可以開始陳述定理內容。設 $\Sigma ,{\hat {\Sigma }}\in \mathbb {R} ^{p\times p}$ 是兩個對稱的隨機矩陣,其特徵值記為 $\lambda _{1}\geq \cdots \geq \lambda _{p}$ 和 ${\hat {\lambda }}_{1}\geq \cdots \geq {\hat {\lambda }}_{p}$ 。對任何 $(r,s):1\leq r\leq s\leq p$ ,考慮第 $\{\lambda _{r},\ldots ,\lambda _{s}\}$ 這總共 $s-r+1$ 個特徵值之對應的特徵向量所張成的線性子空間,將它記為 $V$ ,類似地定義 ${\hat {V}}$ 。
下面定義定理中最重要的量,即**特徵裂隙** $\delta $ : | [
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Davis-Kahan定理 | : $\delta =\inf \left\{|{\hat {\lambda }}-\lambda |:\lambda \in [\lambda _{s},\lambda _{r}],{\hat {\lambda }}\in (-\infty ,{\hat {\lambda }}_{s+1}]\cup [{\hat {\lambda }}_{r-1},\infty )\right\}$
定理的結論是,如果 $\delta >0$ ,那麼有如下不等式:
: $\|\sin \Theta ({\hat {V}},V)\|_{F}\leq {\frac {\|{\hat {\Sigma }}-\Sigma \|_{F}}{\delta }}$
其中 $\|\cdot \|_{F}$ 表示 Frobenius 範數,即將矩陣的所有元素平方求和後,再開根號。
### 定理的 Yu-Wang-Samworth 變體版本
Davis-Kahan 定理的經典版本有一些可改進之處,主要在於正特徵裂隙假設,是一個同時牽涉兩個矩陣的特徵值 $\lambda $ 和 ${\hat {\lambda }}$ 的條件,這對其應用的方便性造成負面影響。余怡、王騰耀和 Richard Samworth 於 2014 年發現如下變體,其最大特色是其只需其中一個矩陣滿足正特徵裂隙條件。
沿用上面經典版本定理的記號,另記 $d=s-r+1$ ,並用如下的特徵裂隙條件代替原定理中的 $\delta >0$ :
: $\min(\lambda _{r-1}-\lambda _{r},\lambda _{s}-\lambda _{s+1})>0$
Yu-Wang-Samworth 定理的結論,按經典版的 $\sin \Theta $ 語言,陳述如下:
: $\|\sin \Theta ({\hat {V}},V)\|_{F}\leq {\frac {2\min \left(d^{1/2}\|{\hat {\Sigma }}-\Sigma \|,\|{\hat {\Sigma }}-\Sigma \|_{F}\right)}{\min(\lambda _{r-1}-\lambda _{r},\lambda _{s}-\lambda _{s+1})}}$
其中, $\|\cdot \|$ 表示矩陣的譜範數,即其最大奇異值。 | [
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] |
Davis-Kahan定理 | 進一步,按矩陣論語言,有如下更顯式的結論:存在一個正交矩陣 ${\hat {O}}\in \mathbb {R} ^{d\times d}$ (「正交」是指其滿足 $O^{T}O=I_{d}$ ),使得:
: $\|{\hat {V}}{\hat {O}}-V\|_{F}\leq {\frac {2^{3/2}\min \left(d^{1/2}\|{\hat {\Sigma }}-\Sigma \|,\|{\hat {\Sigma }}-\Sigma \|_{F}\right)}{\min(\lambda _{r-1}-\lambda _{r},\lambda _{s}-\lambda _{s+1})}}$
## 注意事項
雖然 Davis-Kahan 定理大多數的應用是套用到隨機矩陣上,但要注意定理本身並不局限於隨機矩陣,無論定理內容中出現的矩陣是常數矩陣還是隨機矩陣(抑或是一個確定一個隨機),只要假設條件滿足,定理的結論都成立(而非僅以大概率成立或漸近成立)。
## 應用
Davis-Kahan 定理擁有廣泛的應用,是**譜聚類**方法的理論基礎,在統計學習和統計網絡分析的很多涉及聚類問題的研究中,占據重要地位。
## 參見
特徵裂隙
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] |
腦磁波儀 | **腦磁波儀**(英語:Magnetoencephalography,簡稱 **MEG**)是一種功能性神經成像技術,透過非常靈敏的磁強計紀錄大腦自然產生的電流所產生的磁場,繪製大腦活動的影像。 超導量子干涉儀(superconducting quantum unit interference devices, SQUID)陣列是目前最常見的磁強計,而無自旋交換鬆弛(spin exchange relaxation-free, SERF )磁強計則在進行研究,做為未來使用的儀器。腦磁波儀包括對知覺和認知 MEG 的應用包括對知覺和大腦認知過程的基礎研究,和在手術切除前定位受病理影響的區域,確定腦各部位的功能以及神經回饋。可以應用於臨床上發現異常的位置,也可以應用於實驗上簡單的量測腦部活動。
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特洛伊波包 | **特洛伊波包**(英語:trojan wave packet )是非穩態且不擴散的波包 ,屬於由原子核和一個或多個電子波包所組成的人造系統,受到連續電磁場高度激發。
強烈的偏振電磁場會將電子波包控制住,或是說將其「捕獲」在特意選擇的軌道(能量殼層)中。 波包名稱源自太陽–木星系統中的特洛伊小行星 。 特洛伊小行星位於木星軌道上的拉格朗日平衡點 L4 和 L5,圍繞著太陽運行。它們在此處相位鎖定,避免相互碰撞,而特洛伊波包的結合方式就類似於這種現象。
## 概念與研究
特洛伊波包的概念源自蓬勃發展的物理學領域,物理領域已經可以做到在原子層級上操縱原子和離子,造出可以控制原子的離子阱,進而使用離子阱來創造新的物質形態,包括離子液體、維格納晶體和玻色 - 愛因斯坦凝聚 。 控制量子特性的能力是在現實生活中發展奈米元件(例如量子點和微晶片阱)應用的直接關鍵。2004 年研究表明,造出一個實際上是單原子的阱,並操縱原子內部電子的行為是有可能的。
在 2004 年使用激發態鋰原子進行的實驗中,研究人員能夠將單顆電子定位在 15000 個軌道(900 ns)中的其中一個軌道上,既不會擴散,也不會色散。這種「經典原子」是透過微波場來合成的,藉由 "拴住" 電子,使其運動被相位鎖定在微波場內。這種獨特原子系統中的電子相位鎖定,就類似於上面所堤到的木星軌道的小行星相位鎖定。
這個實驗所探討的技術是對一個早期問題的解決方案,這問題可追溯到 1926 年。當時的物理學家意識到,任何初始的局部波包都將不可避免地擴散到整個電子軌道,物理學家注意到「原子庫侖位能的波方程會產生色散」。到了 1980 年代,幾組研究人員證明了這一點。波包會在軌道上一路擴散開來,並與自己發生相干性干涉。近期透過諸如特洛伊波包等實驗所實現的創新是將波包局部化,亦即沒有發生擴散。該創新是應用了圓偏振電磁場,在微波頻率下與電子波包同步,故意讓電子波包保持在拉格朗日型軌道上。 特洛伊波包實驗是建立在之前激發態鋰原子實驗的工作基礎上,實驗的原子對電場和磁場反應靈敏,衰變周期相對較長,而電子則出於各種意圖和目標,確實運行在經典軌道上。由於偏振微波場可以用來進行控制和響應,因此對電場和磁場的敏感度相當重要。
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特洛伊波包 | 下一個合乎邏輯的步驟是嘗試從單電子波包進展到多電子波包 。而雙電子波包已經在鋇原子中完成這兩個電子波包都是局域化的。但是它們最終在原子核附近碰撞,進而產生色散 。另一種技術採用了一對非色散電子,但其中一顆電子的軌道必須局部化且靠近原子核。這種非色散型雙電子特洛伊波包的演示改變了現況,而這些是單電子特洛伊波包的下一階段類比,專為類比激發氦原子而設計。
到 2005 年 7 月,帶有具相干性、穩定性的非色散型雙電子波包的原子已經被實作了出來。 它們可以是處於激發態的類氦原子或量子點氦(在固態應用中),也可以在原子(量子)尺度上類比於牛頓經典物理學的三體問題。同時,圓偏振電磁場和磁場使在氦原子或量子點氦(帶有雜質中心)的雙電子組態能夠穩定,且在廣闊的電磁波譜內都能維持穩定。因此,這種雙電子波包的組態被認為是真正的非色散性,比如,配置在受到束縛的二維空間量子點氦的電子。現今已經有了各式各樣的雙電子的特洛伊波包組態,而截至 2005 年,只有一個三維空間的配置。 在 2012 年進行了一項重要的實驗步驟,不僅以絕熱變化的頻率生成並鎖定特洛伊波包,也按照 Kalinski 和 Eberly 的預測對原子進行擴張。 透過在絕熱斯塔克場(adiabatic Stark field)中的連續激發,可以在氦中產生雙電子朗繆爾特洛伊波包,先是在 He+
上首次產生圓形單電子環,接著再將第二個電子置於類似的狀態 。
## 參見
* 原子軌道
* 芮得柏態
* 孤波
* 量子疤痕
## 參考文獻
## 進一步閱讀
### 圖書
* March, Raymond E.; John F. J. Todd. Practical Aspects of Ion Trap Mass Spectrometry : Volume I: Fundamentals of Ion Trap Mass Spectrometry. USA: CRC Press. 1995. ISBN 978-0-8493-4452-7.
* March, Raymond E.; John F. Todd. Quadrupole Ion Trap Mass Spectrometry 2. Wiley, John & Sons, Incorporated. 2005 [2020-07-15]. ISBN978-0-471-48888-0. (原始內容存檔於 2020-08-09).
### 期刊文章 | [
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] |
特洛伊波包 | * Sirko, L.; Koch, P. M. The pendulum approximation for the main quantal resonance in periodically driven Hydrogen atoms. Applied Physics B: Lasers and Optics. 1995, **60**: S195–S202.
* Klar, H. Periodic orbits in atomic hydrogen exposed to circularly polarised laser light. Zeitschrift für Physik D. 1989, **11** (1): 45–52. Bibcode:1989ZPhyD..11...45K. doi:10.1007/BF01436583.
* Maeda, H.; Gurian, J. H.; Gallagher, T. F. Nondispersing Bohr Wave Packets. Physical Review Letters. 2009, **102** (10): 103001–103004. Bibcode:2009PhRvL.102j3001M. doi:10.1103/PhysRevLett.102.103001.
* Stroud, C. R., Jr. An astronomical solution to an old quantum problem. Physics. 2009, **2**: 19. Bibcode:2009PhyOJ...2...19S. doi:10.1103/Physics.2.19.
## 外部連結
* Aharonov-Bohm Oscillations In "Trojan Electrons" (頁面存檔備份,存於網際網路檔案館)
[[Category: 量子力学]]
[[Category: 纳米技术]]
[[Category: 纳米电子学]]
[[Category: 微技术]]
[[Category: 半导体器件制造]]
[[Category: 材料科學]] | [
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] |
光譜符號 | 本文是關於原子和分子軌道的符號。它不能與描述多電子系統的類似表示法,羅素–桑德斯能項符號混淆。該術語符號通常也被稱為_光譜符號_。
**光譜符號**提供了一種指定原子的電離狀態、原子軌道和分子軌道的方法。
## 電離狀態
光譜學家通常以元素符號的後面跟隨羅馬數字來顯示電離狀態產稱的頻譜。數字 I 用於與中性元素關聯的光譜線,II 用於有一顆電子被電離狀態的光譜,III 用於二顆電子被電離狀態的光譜,III…… 依此類推。例如,'He I' 表示中性氦,'C IV' 表示碳在 C3+ 狀態的光譜。此表示法用於檢索資料庫:NIST 原子頻譜資料庫(頁面存檔備份,存於網際網路檔案館)。
## 原子和分子軌道
在原子軌道被理解之前,光譜學家在原子光譜中發現各種獨特的光譜線系列,他們用字母來識別這些光譜線,後來這些字母與角量子數 _ℓ_關聯。 "s","p","d" 和 "f" 依序被選為描述角量子數_ℓ_的最初 4 個數值的字母,源自觀測到鹼金屬光譜序列的首字母。其它的_ℓ_後續值按照字母序列排序,但是省略掉字母 "j"。這是因為有些語言中不易區分字母 "i" 和 "j":
:
這種表示法用於指定電子組態,並創建多電子原子的電子狀態的術語符號。在編寫術語符號時,上述單顆電子的軌道量子數的方案會應用於與電子狀態相關的總軌道角動量。
### 分子光譜符號
分子的光譜符號使用希臘字母來表示沿核軸的軌道角動量的模量。The
表示此角動量的量子數為 Λ。
: Λ = 0, 1, 2, 3, ...
: 符號:Σ, Π, Δ, Φ
對於 Σ 的狀態,使用上標面的 "+" 表示包含核(對稱)的平面,"-" 用來表示沒有時的狀態。
對於同核的雙原子分子,註腳 "g" 或 "u" 表示存在元素對稱中心(或反轉中心),並指示振動光譜波函數與點 - 群反轉操作的對稱性 "_i_"。"_i_"的振動狀態是對稱的表示為"g"(德文的 gerade,表示偶數),非對稱狀態表示為 "u"(德文的 ungerade,表示奇數)。
## 相關條目
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量子存储器 | 在量子計算機中,**量子存儲器**即是傳統計算機存儲器的量子力學版本。傳統存儲器將信息存儲為二進位狀態(由「1」和「0」表示),而量子存儲器存儲的是量子狀態。這些量子狀態保存了有效計算信息,稱為量子位元。與傳統計算機的存儲器不同,量子存儲器中的狀態處於量子疊加狀態,使其在量子算法中比傳統存儲器更實用且靈活。
## 類型
### 光量子存儲器
傳統光信號利用改變光的振幅來傳輸信息。因此,我們能用計算機硬碟,甚至是一頁紙來存儲光的信息。然而,在量子信息的情況下,信息由光的振幅和相位編碼。對於一些信號,我們不能同時測量光的振幅和相位。為了存儲這樣的量子信息,我們必須要在不測量的情況下,存儲光的信息。一旦測量,信息就丟失了。光量子存儲器將光的狀態記錄到原子云(atomic cloud)中。當原子吸收了光,原子就保有了光量子的一切信息。
### 固態量子存儲器
在經典計算中,存儲是不太重要的,因為信息可以複製到長期保存的存儲硬體中,未來處理時再取回就好。而在量子計算中,這是禁止的,因為根據不可克隆原理,任何量子態都不能被完全複製。因此,當沒有量子糾錯的情形下,量子位元的存儲被其保持信息的內部耦合時間所限制。除了量子位元保存時長的限制外,將量子信息,在不受環境噪音等其他因素影響的情形下,進行大量快速操作或讀取,也是一大難點。
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电子泡沫 | **電子泡沫**(Electron bubble)是在低溫氣體或液體(如氖氣或氦氣)中的自由電子周圍產生的空白空間。它們通常非常小,在大氣壓下直徑約為 2nm。
## 氦中的電子泡沫
在室溫下,惰性氣體中的電子自由移動,僅受與弱相互作用原子碰撞的影響。它們的遷移率取決於氣體的密度和溫度,這已經通過經典動力學理論較好地描述。隨著溫度的降低,電子遷移率會降低,因為氦原子在低溫下會減慢移動速度,並且不常與電子進行相互作用。[1]
在臨界溫度以下,電子的遷移率迅速下降到遠低於經典預期的值。這種差異導致了電子氣泡理論的發展。[2] 在低溫下,注入液氦的電子不會像人們期望的那樣自由移動,而是在自身周圍形成小的真空氣泡。
## 氦表面的電子排斥
由於氦氣和液相之間的介電常數的差異,電子被液氦吸引。負電子使表面的氦極化,導致鏡像電荷(image charge)將其與表面結合。由於氫原子較為穩定,電子不能進入液體中。電子和鏡像電荷形成一種約束狀態,就像電子和質子在氫原子中一樣,具有最小的平均間隔。在這種情況下,最小能量約為 1eV(原子尺度上適量的能量)。[3] 當電子被迫進入液氦而不是漂浮在其表面時,它會形成氣泡而不是進入液體。氣泡的大小由三個主要因素決定(忽略較小的修正):限制項(confinement term)、表面張力項和壓力 - 體積項。限制項是純粹的量子力學,因為每當電子被嚴格約束時,其動能就會上升。表面張力項代表液氦的表面能,這就像水和所有其他液體一樣。壓力 - 體積項是將氦氣推出氣泡所需的能量。[4]
$$
E\approx {\frac {h^{2}}{8mR^{2}}}+4\pi R^{2}\alpha +{\frac {4}{3}}\pi R^{3}P
$$
這裡 _E_ 是氣泡的能量,_h_ 是普朗克常數,_m_ 是電子質量,_R_ 是氣泡半徑,_α_ 是表面能,_P_ 是環境壓力。
## 2S 電子泡沫
根據對上述方程的分析,對 2S 電子泡沫在廣泛的環境壓力下表現出驚人的形態不穩定性進行了理論預測。雖然其波函數是球形的,但氣泡的穩定形狀是非球形的。[5]
## 外部連結
* Quantum bubbles are the key (新聞稿). New Scientist. 25 November 2005 [2020-07-18]. (原始內容存檔於 2020-07-19).
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] |
能项符号 | **能項符號**是量子力學中描述多電子原子中(總)角量子數的縮寫符號(實際上單個電子也可以用能項符號來描述)。具有給定電子排布的原子的每個能級不僅由電子排布來描述,還由其能項符號來描述,因為能級還取決於包括自旋在內的總角動量。考慮原子的能項符號時,通常假定存在自旋 - 軌道耦合現象。原子的基態能項符號由洪特規則預測。
_能項_一詞的使用是基於里德堡 - 里茲組合原理:頻譜線的波數可以表示為兩個能級之差。後來由玻爾模型進行了總結,該模型確定了具有量子化能級的能項(乘以 _hc_,其中 _h_ 是普朗克常數,而 _c_ 是光速),並確定了與光子能量相關的光譜波數(再次乘以 _hc_)。
## 旋軌耦合與符號
對於輕原子,自旋 - 軌道相互作用很小,因此總角量子數 L 和總自旋量子數 S 是好量子數。 L 和 S 之間的相互作用稱為 LS 耦合(自旋 - 軌道耦合)或 Russell-Saunders 耦合(以 Henry Norris Russell 和 Frederick Albert Saunders 的名字命名,他們在 1925 年對此進行了描述)。用以下形式的能項符號可以很好地描述原子狀態:
:
其中
: _S_ 為總自旋量子數,2_S_+1 為自旋多重度,表示 _L_≥_S_ 條件下,對給定 _L_ 和 _S_,總角動量量子數 _J_ 的可能狀態數。(如果 _L_<_S_,則可能的 _J_ 的最大數目為 2_L_+1)這可以通過式 _J_max = _L_ + _S_ 與 _J_min = |_L_ − _S_| 很容易地證明:_J_ 的可能狀態數為 _J_max − _J_min + 1。
: _L_ 是總角量子數的光譜符號。前 17 個角量子數對應的光譜符號為:
: : | [
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] |
能项符号 | S、P、D、F 四個符號是根據與 s、p、d、f 軌道對應的光譜線的特性得出的:銳線系(sharp)、主線系(principal)、漫線系(diffuse)和基線系(fundamental);其餘的按字母順序從 G 開始命名,只是省略了 J。當用於描述原子中的電子狀態時,能項符號通常遵循電子構型。 例如,碳原子的一個低能級的能項符號表示為 1s22s22p2 3P2。 上標 3 表示自旋狀態是三重態,因此 _S_=1(2_S_+1=3),P 是 _L_=1 的光譜符號,下標 2 是 _J_ 的值。使用相同的規則,可將碳的基態表示為 1s22s22p2 3P0。
## 腳註
## 參考文獻 | [
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自旋多重度 | 在光譜學和量子化學中,能級的**自旋多重度**定義為 2_S_+1,其中 _S_ 是總自旋角動量。自旋多重度為 1、2、3、4、5 的狀態分別稱為單重態,雙重態,三重態,四重態和五重態。
## 原子
對於原子,自旋多重度通常等於總自旋相對於總軌道角動量 _L_ 的可能取向的數量,因此等於僅因自旋 - 軌道作用而導致能量差異的近簡併能級的數量。
例如,碳原子的基態是 3P 態。上標 3(讀作三重態)表示自旋多重度 2_S_+1=3,因此總自旋量子數 _S_=1。這種自旋歸因於兩個不成對的電子依據洪特規則以相同的自旋方向填充簡併軌道。組成三重態的三個狀態沿著總軌道角動量方向的自旋分量分別為 + 1、0 和–1,總軌道角動量為為 1,如字母 P 所示。總角動量量子數 _J_ 的最值分別為 _L_+_S_=2 與 _L_-_S_=0,每兩個可能的 _J_ 之間相隔 1,因此 _J_=2、1 或 0。
但是,僅當 _S_≤_L_ 時,自旋多重度才等於自旋方向的數量。當 _S_>_L_ 時,總角動量只可能有 2_L_+1 個方向,範圍從 _S_+_L_ 到 _S_-_L_。氮原子的基態為 4S 四重態,有三個不成對的電子,由 2_S_+1=4 得 _S_=3/2。對於光譜符號為 S 的態,_L_=0,因此 _J_ 只能為 3/2,即使自旋多重度為 4,該態也只有一個能級。
## 分子
穩定的有機分子具有完整的電子殼層,沒有不成對的電子,因此基態均為單重態。對於僅包含主族元素的無機分子也是如此。重要的例外是氧分子(O2)以及亞甲基卡賓(CH2)等卡賓。
然而,具有較高自旋的基態在過渡金屬的配合物中非常普遍。晶體場理論提供了這種配合物自旋態的簡單解釋。
### 氧分子
氧分子的 HOMO(最高占據分子軌道)是一對簡併的 π\* 軌道。基態下,該能級被自旋同向的兩個電子占據。因此,該分子基態下處於三重態。
而氧分子的第一激發態在 π\* 能級具有兩個自旋相反的電子,因此不存在自旋不成對的電子,是單重態,被稱為單重態氧。
### 亞甲基卡賓
在有機化學中,卡賓是碳原子僅具有六個價電子的分子,因此不遵守八隅律。卡賓通常以其自旋多重性分為單線態和三線態。兩者都有兩個非鍵合電子,差別在於:在單線態卡賓中,這些電子以孤電子對形式存在並且自旋相反,因此沒有淨自旋;而在三線態卡賓中,這些電子具有自旋平行。
## 參考文獻
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自旋多重度 | * Atkins, Peter; de Paula, Julio. Atkins' Physical Chemistry 8th. United States: Oxford University Press. 2006. ISBN 0-7167-8759-8.
* Clayden, Jonathan; Greeves, Nick; Warren, Stuart; Wothers, Peter. Organic Chemistry. United States: Oxford University Press. 2001. ISBN 0-19-850346-6.
* Levine, Ira N. Quantum Chemistry 4th. United States: Prentice-Hall. 1991. ISBN 0-205-12770-3.
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拉波特规则 | **拉波特規則**(Laporte rule)是一種僅適用於中心對稱分子或原子的光譜選律,可以表述為:相同原子軌道(例如 _s_-_s_,_p_-_p_,_d_-_d_ 或 _f_-_f_)之間的躍遷是禁阻的。此規則也可表述為:宇稱不變或保留相對於反演中心的對稱性的躍遷是禁阻的,即躍遷前後電子所在軌道的對稱性不能均為對稱(_g_)或均為反對稱(_u_)。此類分子中允許的躍遷必須涉及宇稱的變化,即 _g_→_u_ 或 _u_→_g_。
符號 _g_ 表示相對於反演中心對稱,意即:如果分子中的所有原子都關於反演中心進行反轉,那麼反轉後的軌道與反轉前完全一樣(包括空間取向相同)。符號 _u_ 意味著軌道相對於反演中心是反對稱的,在反演後各處都會改變符號。該規則源於量子力學選律:電子躍遷期間,宇稱應反轉。
但是,如果分子的對稱中心被破壞,則允許進行禁阻躍遷,實際上,在實驗中觀察到了這種明顯禁阻的躍遷。對稱中心的破壞由於各種原因而發生,例如姜 - 泰勒效應和不對稱振動。分子並非始終都是完全對稱的,由於分子的不對稱振動而發生的躍遷稱為振動躍遷,例如由非絕熱耦合引起的躍遷。通過這樣的非對稱振動,理論上禁阻的躍遷(例如 _d_→_d_ 躍遷)被弱允許了。
該規則以奧托・拉波特的名字命名,與過渡金屬的電子光譜有著密切關係。八面體絡合物具有對稱中心,故根據該規則,_d_→_d_ 躍遷是禁阻的,且實際觀察到其吸收非常弱。但是,四面體絡合物沒有對稱中心,因此拉波特規則不適用,光譜吸收較八面體絡合物更強。
## 參見
* 選律
* 田邊 - 菅野圖
* 配位場理論
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选择定则 | **選律**是物理和化學中,從形式上限制系統從一種量子態到另一種量子態的可能躍遷的定則。對於分子,原子,原子核等內部的電磁躍遷,均存在相關的選律。選律受觀察躍遷時所使用的技術影響,同一躍遷使用不同手段觀測時可能適用不同的選律。化學反應中也存在選律,例如:從反應物到生成物的轉化過程中自旋狀態發生改變的反應在形式上是自旋禁阻的。 | [
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超选择定则 | 量子力學中,**超選擇定則**是希爾伯特空間上的自伴算子為可觀察量的必要條件。對於自伴算子 ${\hat {A}}$ ,若存在滿足超選擇定則的算子 ${\hat {J}}$ ,使 $[{\hat {A}},{\hat {J}}]=0$ ,則 ${\hat {A}}$ 滿足超選擇定則。反之,逆命題「滿足超選擇定則的算子是可觀察量」是否為真命題則尚不明確。 | [
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关联成像 | **量子成像**(英語:Quantum Imaging,QI),又稱**鬼成像**(英語:Ghost Imaging,GI)、**關聯成像**(英語:Correlated imaging,CI)等,是一種利用光場的二階或高階關聯獲得物體資訊的成像方法。量子成像屬於非定域成像,其概念起源於 20 世紀 50 年代的 HB-T 實驗。繼纏結光量子成像實驗之後,陸續有研究者提出了古典光量子成像、無透鏡量子成像、計算量子成像、差分量子成像等技術。量子成像技術在光刻、雷射雷達、生物組織造影、水下成像等領域都有應用。
## 歷史
### 基礎研究
20 世紀 50 年代,漢伯里・布朗(英語:R. Hanbury Brown)與特威斯(英語:R. Q. Twiss)進行了 HB-T 實驗,其主要內容是設計了一種干涉儀以解決在基線較長的情況下,無線電星角直徑的測量問題。這種干涉儀在無線電天文學中又被稱為強度干涉儀,其大致結構是:來自光源的光被半鍍銀鏡分為兩束,分別照射兩個光電倍增管的陰極,兩管的輸出電流經過放大以後在線性混頻器中相乘,如此持續運行大約一小時以獲得可觀測的結果。因此其在形態上類似邁克生干涉儀,但不同點在於,邁克生干涉儀是在檢測之前混合兩路信號,並且信號在混合之前始終擁有相位資訊。這種干涉儀則不然,進行混合的只是兩路信號的強度,相位資訊在經過光電倍增管之後已經被抹去了。但即便如此,兩路信號仍然表現出相干性,這意味著光場的相干性不僅在相位上體現出來,甚至僅僅在強度上也可以體現。文章發表之後,一些物理學家無法在 HB-T 實驗驗證中得出顯著的相干性,並聲稱「這種相干性的存在要求對量子力學中一些基本概念進行重大修訂」。漢伯里・布朗和特威斯進行了理論推導,並嘗試了對天狼星 A 的觀測,最終驗證了實驗結果的合理性。這個實驗將光子符合探測引入光學實驗,使得人們認識到光的二階干涉效應會造成光場的強度關聯(相關性)。 | [
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关联成像 | 1970 年,美國國家宇航局電子研究中心的大衛・伯納姆(英語:David Burnham)與唐納德・溫伯格(英語:Donald Weinberg)在光子計數實驗中使用了名叫「自發參量下轉換」的非線性光學技術。兩人用氦 - 鎘雷射器產生 325nm 雷射束泵浦 25mm 長的磷酸二氫銨(ADP)晶體,測得入射光子轉化為相位匹配(入射光子動量和能量等於兩出射光子動量和與能量和)的雙光子的機率最大。這一技術使得纏結光子對可以很方便地獲得。1985 年以後,人們開始注意到自發參量下雙光子場的存在,並開始對其進行研究和應用。1988 年,蘇聯學者大衛・尼古拉耶維奇提出了一種用來驗證愛因斯坦 - 波多爾斯基 - 羅森實驗,並證明互補原理的方法,其中設計的一種裝置實際上可以作為量子成像設備使用。這種裝置進行符合檢測的方法是,用兩路探測器中的一路是否收到光子,來控制另一路探測的開閉。大衛・尼古拉耶維奇也由此被認為是量子成像方案的提出者。
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关联成像 | 1994 年,大衛・尼古拉耶維奇在一篇嘗試同時使用古典表述和量子表述解釋光的量子性質的論文中,從量子力學的角度闡釋了雙光子非定域成像的理論基礎。1995 年,美國馬里蘭大學的史硯華小組以纏結雙光子作為光源,結合符合測量技術,實現了量子成像。史硯華小組用波長 351.1nm 的氬離子雷射器產生直徑 2mm 的光束作為泵浦源,泵浦被切割成為簡併 II 型相位匹配角的 ${\ce {\beta-BaB2O4}}$ (偏硼酸鋇,BBO)晶體,出射兩路正交偏振信號。分別將從 BBO 晶體的 e - 射線平面和 o - 射線平面出射的光束稱為信號光和閒置光,這兩路光的波長均為 702.2nm,即泵浦光波長的二倍。混合有未經自發參量下轉換的原泵浦光、信號光和閒置光的混合光束經過紫外級熔融石英色散稜鏡濾除剩餘的波長為 351.1nm 的原泵浦光,進入作為偏振分束器的湯普森稜鏡將信號光和閒置光分開。信號光束照射焦距為 400mm 的成像凸透鏡,透過的光束經過一個簡併波長為 702.2nm、帶寬為 83nm 的濾光片,再照射在物體(寫有「UMBC」字樣的光圈)上。經過物體之後,信號光束再通過一個焦距為 25mm 的收集凸透鏡,到達一個直徑為 0.8mm 的乾冰冷卻雪崩光電二極體 D1,這個雪崩光電二極體恰位於收集透鏡的焦點上。閒置光束經過另一個同樣的濾光片,不經過物體,直接照射在由 0.5mm 多模光纖尖端上,再到達另一個乾冰冷卻雪崩二極體 D2。兩個正交的編碼驅動檢測器在垂直於光束方向的平面上進行掃描,並將檢測器的輸出脈衝發送到接收窗口為 1.8ns 的符合計數器。設成像透鏡到收集透鏡距離為 S,成像透鏡到多模光纖尖端距離為 S',成像透鏡焦距為 f,當三者滿足關係式 | [
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关联成像 | 時,裝置可產生清晰物像。其中符合計數器的原理是,兩探測器均有響應時才計數,如果只有一個有響應或都沒有響應則不計數。探測器 D1 沒有空間解析度,D2 所在的閒置光(參考光)光路中沒有待成像物體,所以兩者都不能單獨完成物體成像;但處於無物體參考光路的 D2 探測器經過逐點掃描再與 D1 結果關聯之後得到了物體的像,使得量子成像又被稱為「鬼」成像。1997 年,索托・里貝羅(英語:P. H. Souto Ribeiro)小組發現,當自發參量下轉換晶體足夠薄(在泵浦光傳播方向上足夠短)時,泵浦光束的角頻譜將轉化為自發參量下轉換過程生成的雙光子狀態。小組通過將自發參量下轉換光束的橫向特性與泵浦光束的橫向特性聯繫起來,提出了控制信號光子與閒置光子之間橫向空間相關性的方法,實現了對纏結光子關聯性質的調製,使得在不向信號光路和閒置光路添加任何光學器件的情況下,也可以控制符合檢測入射光束的橫向特性,而不對強度產生影響。
### 古典光量子成像
史硯華小組實驗驗證量子成像之後,古典光是否能實現量子成像在學術界產生了爭議。2001 年,波士頓大學的艾曼・阿布瓦迪(英語:Ayman F. Abouraddy)小組分別用古典光和纏結光進行了量子成像實驗,之後發表評論稱,纏結光可以成部分相干像或者甚至完全相干像,古典光只能成非相干像;量子成像是纏結光的特性,其他雙光子源並不能模仿。然而,2002 年,羅切斯特大學的瑞安・本寧克(英語:Ryan S. Bennink)團隊就使用隨機掃描雷射光源證明了了古典光源也可以進行量子成像。Bennink 團隊對連續雷射束進行斬波,通過隨機旋轉反射鏡產生不同方向的偏轉光,再通過分束器來產生古典光源;用桶探測器檢測信號光是否未被測試圖案遮擋,並記錄信號光未被遮擋時 CCD 拍攝參考光記錄下的幀,即用桶探測器門控 CCD。實驗結果是,未門控時 CCD 無法拍攝到圖案,經過門控之後 CCD 可以拍攝到測試圖案。這證明了,儘管古典光源沒有纏結光源所特有的一些全局性質,但具有一定相關性的古典光源仍然可以通過符合計數產生量子成像現象。 | [
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关联成像 | 2004 年,義大利的路易吉・盧吉亞托小組提出了熱光源的量子成像理論方案。在這種方案中,來自熱光源的光束被分束器分為兩束,後續處理與纏結光源成像相同,小組通過類比纏結光源和熱光源的成像過程,推斷可以使用純粹的非相干光源(熱光源)實現量子成像。2005 年,史硯華小組用氦氖雷射器產生的雷射入射旋轉毛玻璃盤產生的贗熱光源為光源,發現了非纏結光源的雙光子成像高斯薄透鏡方程式,實現了量子成像。同年,中科院物理所的吳令安小組實現了真熱光的雙光子二階關聯,不久後用 20mA 直流供電、諧振波長 780nm 的空心陰極燈(銣燈)實現了真熱光源量子成像。
儘管已經證明無論古典光源還是纏結光源都可以進行量子成像,但費里(F. Ferri)小組於 2005 年發表文章稱,成像的解析度具有一個上限,這個上限只有使用纏結光源可以達到。這證明,纏結光源相對古典光源量子成像,具有資訊可見性和解析度更高的優勢,這種優勢在高精度測量和量子通信領域都有應用。另一方面,熱光源更容易生成和測量,但成像的解析度會更低,背景雜訊更強。
2008 年,美國麻省理工學院教授傑弗里・夏皮羅使用高斯態光模型理論對量子成像原理進行了統一的解釋。
### 無透鏡量子成像
2004 年,韓申生和程靜提出可以通過適當選擇成像幾何形狀,用非相干光源實現無透鏡傅立葉變換成像。這為非可見光量子成像,如 X 射線繞射成像,提供了理論上的可行性。2006 年,史硯華小組實現了無透鏡或其他等效成像系統的贗熱光源量子成像,這種方案適合任何波長的輻射作為光源,並且形成圖像的過程中不需要任何成像透鏡,因此這種方案對於 X 射線、伽瑪射線和其他波長光源的成像應用幫助很大。
### 計算量子成像
夏皮羅也提出了計算量子成像的理論。與傳統量子成像不同,計算量子成像方案僅保留了包含待成像物體的測量光路和桶探測器,通過雷射照射空間光調製器產生可調強度、相位等參數的空間調製光場(又稱為主動式光源),再根據繞射理論計算得到原參考光路在無透鏡量子成像中可以得到的特定位置的光強分布,與測量光場進行符合關聯得到圖像。這種方案所用的裝置可以生成沒有背景雜訊的圖像,其解析度和成像區域可以通過調整空間光調製器的參數來控制。2009 年,以色列科學家 B. Sun 等人在 3D 成像實驗中驗證了計算量子成像的可行性。
### 差分量子成像 | [
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关联成像 | 2010 年,義大利學者路易吉・盧賈托等提出差分量子成像(差分鬼成像,英語:Differential Ghost Imaging,DGI)的方案,該方案提高了量子成像信噪比的數量級,大幅提高了量子成像的成像質量,在一些強幹擾和背景雜訊較大的環境下表現較為良好,但需要大量的測量數據和更複雜的計算。2012 年,羅開紅及其同事提出一種名為「對應成像」(英語:Correspondence Imaging,CI)的技術,可概述為選擇桶探測器在正向或負向的強度波動(正信號與負信號),對對應的參考光路所得的數據進行條件平均,而不是用桶探測器獲得的光強與參考光路所得數據直接相乘。2013 年,中科院物理研究所吳令安小組提出時間對應差分量子成像,將差分量子成像和對應成像的優點結合起來,降低了數據處理難度,縮短了成像所需的計算時間。
## 原理
以下嘗試分析史硯華小組 1995 年所做的纏結光源量子成像實驗,簡述量子成像的原理。
自發參量下轉換過程之後,泵浦光子分裂成為一對信號光子 - 閒置光子,其能量滿足
其中 $\omega _{s}$ 是信號光子的能量, $\omega _{i}$ 是閒置光子的能量, $\omega _{p}$ 是泵浦光子的能量,「 $\cong $ 」代表近似等於。雙光子的的橫向位矢和動量 EPR $\delta $ 函數表達式分別為 | [
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关联成像 | 和其中, ${\overrightarrow {\rho _{s}}}$ 和 ${\overrightarrow {\rho _{i}}}$ 分別是信號光子和閒置光子的位矢, ${\overrightarrow {k_{s}}}$ 和 ${\overrightarrow {k_{i}}}$ 分別是信號光子和閒置光子的動量。雖然光子可能從非線性晶體表面的任何一點出射,但 $\delta ({\overrightarrow {\rho _{s}}}-{\overrightarrow {\rho _{i}}})$ 表明,如果在某一空間位置找到信號 - 閒置光子對中的一個光子,則必在對應位置找到另一個光子,即光子對必從同一點出射。 $\delta ({\overrightarrow {k_{s}}}+{\overrightarrow {k_{i}}})$ 定義了光子對的角度相關性: ${\overrightarrow {k_{s}}}=-{\overrightarrow {k_{i}}}$ ,即雙光子必在相對出射點大致相等但相反的角度存在。
定義 $G^{(2)}({\overrightarrow {\rho _{o}}},{\overrightarrow {\rho _{i}}})$ ; ${\overrightarrow {\rho _{o}}}$ 和 ${\overrightarrow {\rho _{i}}}$ 是物平面和像平面上點的橫向位矢。以下將證明,物平面和像平面之間存在一個 $\delta $ 函數,即存在一種「點對點」的對應關係,若在物平面上 ${\overrightarrow {\rho _{o}}}$ 位置找到信號光子,則必在滿足 $\delta ({\overrightarrow {\rho _{s}}}-{\overrightarrow {\rho _{i}}}/m)$ 關係的位置找到閒置光子。 $m=-{\frac {s_{i}}{s_{o}}}$ ,是像對物體的放大倍數,其中 $s_{o}$ 是物平面與透鏡的光學距離, $s_{i}$ 是像平面與透鏡的光學距離。 | [
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关联成像 | 確定 $\delta $ 函數對應的相關性後,以下展示物函數 $A({\overrightarrow {\rho _{o}}})$ 如何轉到 $A({\overrightarrow {\rho _{i}}}/m)$ 。上圖中的一條「光線」實際上表示一對信號 - 閒置光子。 $(r_{1},t_{1})$ 和 $(r_{2},t_{2})$ 在物平面和像平面上的對應關係實際上是雙光子振幅疊加的結果。
建立格林函數 $g({\overrightarrow {k_{s}}},\omega _{s},{\overrightarrow {\rho _{o}}},z_{o})$ 和 $g({\overrightarrow {k_{i}}},\omega _{i},{\overrightarrow {\rho _{2}}},z_{2})$ 。信號光路和閒置光路的測量方法非常不同,需要分開考慮。
### 信號光路
在信號光路,信號光在從源輸出到成像透鏡的 $d_{1}$ 的距離上自由傳播,通過 $s_{o}$ 距離的物光路,到達收集透鏡,再聚焦到 $D_{1}$ 上,光學傳遞函數為: | [
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关联成像 | ${\overrightarrow {\rho _{s}}}$ 和 ${\overrightarrow {\rho _{l}}}$ 分別是光源輸出平面和成像透鏡平面上定義的橫向位矢。上式中,前後兩個大括號分別代表光子從輸出平面到成像透鏡平面,和成像透鏡平面到物平面的自由空間傳播過程。 $e^{i{\frac {\omega _{s}}{2cd_{1}}}\left\vert {\overrightarrow {\rho _{s}}}-{\overrightarrow {\rho _{l}}}\right\vert ^{2}}$ 和 $e^{i{\frac {\omega _{s}}{2cs_{o}}}\left\vert {\overrightarrow {\rho _{l}}}-{\overrightarrow {\rho _{o}}}\right\vert ^{2}}$ 是菲涅爾相位。把成像透鏡視為薄透鏡,則其變換函數近似為一個高斯函數 $l(\left\vert {\overrightarrow {\rho _{l}}}\right\vert ,f)\cong e^{-i{\frac {\omega }{2cf}}\left\vert {\overrightarrow {\rho _{l}}}\right\vert ^{2}}$ 。
### 閒置光路
在閒置光路,閒置光從源輸出到成像透鏡,整個 $d_{2}$ 距離上都是自由傳播的,光學傳遞函數為:
${\overrightarrow {\rho '_{s}}}$ 和 ${\overrightarrow {\rho _{2}}}$ 分別是源平面和 $\delta $ 光電探測器平面上的橫向位矢。
### 全光路(物平面 - 像平面) | [
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关联成像 | 為簡化計算,假設 $\omega _{s}=\omega _{i}=\omega $ ,SPDC 雙光子共線,忽略所有比例常數(因此將 $=$ 替換為 $\propto $ ),將 $g({\overrightarrow {k_{s}}},\omega _{s},{\overrightarrow {\rho _{o}}},z_{o})$ 和 $g({\overrightarrow {k_{i}}},\omega _{i},{\overrightarrow {\rho _{2}}},z_{2})$ 代入像平面有效波函數(英語:effective wave function)
可求出雙光子有效波函數表達式
完成二重積分
後,雙光子有效波函數表達式變形為
完成對 $d{\overrightarrow {\rho _{s}}}$ 的積分後,可變形為
用 $s_{i}$ 代替 $d_{1}+d_{2}$ , $d{\overrightarrow {\rho _{l}}}$ 上的積分在物平面和像平面之間產生的點對點對應關係,由高斯薄透鏡方程式定義:
用 ${\overrightarrow {\rho _{2}}}$ 等效代替 ${\overrightarrow {\rho _{i}}}$ ,則上式中的積分值趨向無窮大,應用高斯薄透鏡方程式
將 $m={\frac {s_{i}}{s_{o}}}$ 定義為成像系統放大倍數, $\delta ({\overrightarrow {\rho _{o}}}+{\frac {\overrightarrow {\rho _{i}}}{m}})$ 表示物平面上的每一個 ${\overrightarrow {\rho _{o}}}$ 與像平面上的每一個 ${\overrightarrow {\rho _{i}}}$ 唯一對應,兩向量方向相反,大小比為 $m={\frac {\left\vert {\overrightarrow {\rho _{i}}}\right\vert }{\left\vert {\overrightarrow {\rho _{o}}}\right\vert }}$ 。
考慮到成像透鏡尺寸有限(設半徑為 R),則積分會產生點擴散函數 $somb(x)$ : | [
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关联成像 | 其中 $somb(x)=2J_{1}(x)$ , $J_{1}(x)$ 是一階貝索函數,將物 - 像平面的點對點關係轉化為點對像素關係,限制了成像的空間解析度。在代入高斯薄透鏡方程式後,橫向雙光子有效波函數近似為一個 $\delta $ 函數:
這表現了物 - 像平面之間的點對點相關性,即若在物平面 ${\overrightarrow {\rho _{o}}}$ 位置找到信號光子,則必然在像平面 ${\overrightarrow {\rho _{i}}}$ 位置找到閒置光子, ${\overrightarrow {\rho _{o}}}$ 和 ${\overrightarrow {\rho _{i}}}$ 滿足 ${\overrightarrow {\rho _{o}}}+{\frac {\overrightarrow {\rho _{i}}}{m}}=0$ , $m={\frac {s_{i}}{s_{o}}}$ 。
在信號光路的光學傳遞函數中再加入作為物體的光圈、收集透鏡和光子計數檢測器,其中後兩者整體可視為一個桶探測器。桶探測器對通過物體(光圈) $A({\overrightarrow {\rho _{o}}})$ ,觸發光電聯合檢測的光子進行積分:
同時,閒置光路中的探測器 $D_{2}$ 再次掃描像平面, ${\displaystyle {\overrightarrow {\rho _{2}}}}={\displaystyle {\overrightarrow {\rho _{i}}}}$ 。
綜上所述,位置 EPR 相關性是雙光子振幅相干疊加的結果:
原則上,一對信號 - 閒置光子對包含用於在物平面和像平面間產生點對點對應關係的雙光子振幅,因此量子成像又稱為「雙光子關聯成像」。
## 相關領域與應用
### 光刻技術 | [
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关联成像 | 2000 年,博托(英語:A. N. Boto)小組提出了 N 光子吸收光刻技術,這種技術使用纏結光子流取代古典光的非相干性光子流,降低光刻技術中的最小可分辨特徵尺寸。高度纏結的光子可以使得光刻技術的最小可分辨特徵尺寸突破瑞立繞射極限規定的最小值 $\lambda /2$ ,達到 $\lambda /2N$ (N 是一個泵浦光子分裂成為的一組纏結光子的數量,這些光子最後都會被光刻膠吸收)。其原理可以簡述為:在古典光中,N 個光子到達某一特定空間區域的機率是單個光子到達該範圍的 N 次方,但纏結光中只要確定其中一個光子到達的區域,其他 N-1 個光子會到達的區域是確定的,如果光學系統對的足夠准,則 N 個纏結光子到達某一特定區域的機率就只需要計算一次,這使得 N 光子光刻不需要光焦度達到不切實際的程度,僅使用與古典器件相同的功率級別,即可使光刻最小可分辨特徵尺寸降低 N 倍。
### 雷射雷達技術
傳統雷射雷達分為兩種類型:掃描成像雷射雷達和非掃描成像雷射雷達。掃描成像雷射雷達通過用脈衝雷射逐點掃描目標區域來獲得目標的真實空間圖像,這種雷達難以對高速運動物體進行成像;非掃描成像雷射雷達用脈衝閃光雷射源和高解析度成像系統進行成像,一次曝光即可獲得目標的真實空間圖像,但目標反射的光強是由 CCD 相機許多小像素接收到的,因此檢測靈敏度較低,其檢測距離受到成像系統光路和整個成像平面的信噪比的影響。相較之下,量子成像雷射雷達具有遙感距離長、成像速度快和成像解析度高等優點。
2009 年,以色列科學家亞倫・希爾伯格(英語:Yaron Silberberg)等進行了計算量子成像的驗證實驗,提出了用於贗熱量子成像的圖像重建高級算法,並提出計算量子成像可以用於雷射雷達。2011 年,美國麻省理工學院學者提出計算量子成像用於遙感成像的方案,並分析了這種方案的性能。2012 年,上海光機所韓申生團隊實現了基於稀疏約束的關聯成像雷達,並在約 1km 的距離上進行了高解析度成像。2013 年,韓申生團隊實現了 3D 量子成像雷射雷達。2015 年,韓申生小組提出了結構化圖像重構方法,這種方法可以更準確地恢復具有各種稀疏比率的場景切片,並且具有明顯的增強解析度的效果,這適用於測量次數較少的量子成像過程,大幅提高了三維量子成像雷射雷達的成像質量。2016 年,清華大學戴瓊海小組提出了內容自適應計算量子成像方法,用以在測量次數較少的情況下重建較高質量的圖像,從而完成對動態目標的成像。 | [
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] |
关联成像 | ## 參見
* 量子力學
* 量子力學入門
* 量子光學
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] |
豪威科技 | **OMNIVISION** 是一個全球性的無晶圓廠半導體企業,由台灣奧斯來科技成立於 1995 年,目前是一家在美注冊的中資公司,致力於設計和開發先進的數位成像技術和產品,從事圖像感測器設計、研發和市場銷售的數位影像處理方案,用於智慧型手機、手提電腦、平板電腦、攝像頭、娛樂設備、安防系統、汽車和醫療成像系統等。
OMNIVISION 總部位於美國加州聖克拉拉,在美國、歐洲和亞洲各國設有卅餘個辦事處,並在挪威、比利時、日本、新加坡、中國和美國,全世界總共設有 10 個研發中心。
2000 年豪威科技在納斯達克上市,2016 年,豪威科技由中信資本、北京清芯華創和金石投資組成的中國財團收購。2018 年 4 月,韋爾股份重啟了對豪威科技的收購,並於 2019 年 5 月通過了證監會的審核,成功收購了北京豪威科技及其他相關資產。OMNIVISION 互補式金屬氧化物半導體感光元件 CMOS 市佔率為全球第三,僅次於索尼和三星。
## 公司沿革
OMNIVISION 公司的重要里程碑如下:
* 1995 年:由奧斯來科技所創立。
* 1999 年:第一個特定應用積體電路(ASIC)。
* 2000 年:首次公開上市募股(IPO)。
* 2005 年:收購 CDM-Optics 公司,該公司為實現波前編碼商業化而成立。
* 2010 年:收購 Aurora Systems,並將 LCOS 加入其產品線。
* 2011 年:收購柯達專利。
* 2015 年:2015 年 4 月簽署協議後,被一批中國投資機構收購,其中包括中信資本、北京清芯華創和金石投資,收購價格約為現金 19 億美元。
* 2016 年:由於被中國私募股權財團收購,而下市成為一家私人公司。
* 2019 年:韋爾半導體以 21.78 億美元收購 OMNIVISION 和 SuperPix Micro Technology,並將其合併為 Omnivision 集團。
* 2019 年:OV6948 獲得世界上最小的商業化感測器金氏世界紀錄 。
* 2022 年:豪威科技 OmniVision Technologies 更名為 OMNIVISION,並增加了兩個新的業務部門:類比解決方案和觸控與顯示解決方案。
## 技術
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豪威科技 | OMNIVISION 的正面照明(Front-Side Illumination,FSI)技術用於製造小型相機,其裝置於智慧型手機、筆記型電腦和其他需要低光效能而無需閃光燈的應用。
OmniPixel3-GS 在其前身的基礎上進行擴展,用於面部認證的眼動追蹤,以及其他電腦視覺應用。
### OmniBSI
背面照明影像(Back-Side Llluminated,BSI)技術與 FSI 架構的不同之處,在於如何將光線傳遞到感測器的光敏區。在 FSI 架構中,光線必須首先通過電晶體、電介質層和金屬電路。相反地,OmniBSI 技術將影像感測器倒過來,在像素的背面應用彩色濾光片和微透鏡,從而通過感測器背面收集光線。
### OmniBSI-2
第二代 BSI 技術由 OMNIVISION 與 TSMC 台灣積體電路製造合作開發,採用客製化的 65 奈米設計規則和 300 毫米銅製程製造,這些技術的改變是為了改善低光靈敏度、暗電流和電位能井容量,並提供更清晰的影像。
### CameraCubeChip
在相機模組中,感測器和鏡頭的製造過程採用半導體堆疊方法,透過結合 CMOS 影像感測器、晶片級封裝製程(Chip Scale Packaging,CSP)和晶圓級微透鏡(Wafer-Level Optics (頁面存檔備份,存於網際網路檔案館),WLO)的單一步驟,製造出晶圓級光學元件。這些完全整合的晶片產品,具有相機功能且有助於生產體積輕薄短小的裝置。
### RGB-Ir 技術
RGB-Ir 技術使用彩色濾光片製程提高色彩的保真度,透過將其像素陣列圖案的 25% 投入到紅外線,75% 投入到三原色光模式,可同時捕獲三原色光模式和紅外線影像,使其有能力用同一個感測器,捕捉白天和夜晚的影像。該技術用於以電池供電的家庭保全攝影機,以及生物識別,如手勢和面部識別。
### PureCel 技術
OMNIVISION 開發了 PureCel 和 PureCel Plus 影像感測器技術,為智慧型手機和運動攝影提供更多的攝影功能,目標是提供更小的相機模組,其可實現更大的光學格式,並提供更好的影像品質,尤其是在低光照條件下的品質。 | [
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豪威科技 | 這兩種技術都是以堆疊晶片的形式提供(PureCel-S 和 PureCelPlus-S),這種堆疊式晶片方法將成像陣列與影像感測器處理管道分離成一個堆疊式晶片架構,可以在感測器上實現額外功能,且與非堆疊式感測器相比,提供了更小的晶片尺寸。PureCelPlus-S 使用部分深溝隔離(Deep Trench Isolation,B-DTI)結構,其包括介面氧化物、首次沈積的 HfO、TaO、氧化物、Ti 基襯墊和鎢芯。這是 OMNIVISION 的第一個 DTI 結構,也是自 2013 年以來第一個金屬填充的 B-DTI 溝槽架構。
PureCel Plus 使用埋藏式彩色濾光片陣列(Buried Color Filter Array,BCFA)來收集各種入射光角度的光線,以提高容差,深溝隔離通過在晶片內部的像素之間建立隔離牆來減少串擾耦合。
在 PureCel Plus 第二代中,OMNIVISION 為實現更好的像素隔離和低光效能,著手改進深溝隔離,其目標應用為智慧型手機攝影鏡頭。
### DCG HDR 技術
OMNIVISION 開發了其獨特的 DCG 技術,以擴大影像感測器的動態範圍,並在具有挑戰性的照明條件下實現準確的場景再現。它採用了光生電荷的雙重採樣,同時具有像素級的高低轉換增益,高轉換增益讀出能夠降低讀取雜訊,而低轉換增益能夠實現更高的全井容量,擴展了影像感測器的低光範圍,提供準確、低雜訊和無移動性假象的 HDR 畫面擷取。
### SCG 技術
SCG 技術能夠在所有照明條件下,實現最佳影像品質和最佳訊號雜訊比。
透過將高、低轉換增益與 SCG 開關相連接,即可啟動選擇性電荷檢測,以獲得最佳讀出路徑。額外的轉換增益和 SCG 開關可以在一個影像感測器中容納極亮和極暗的影像讀出,同時提供出色的影像品質。
該技術使影像感測器能夠選擇最佳的讀出路徑,以消除極亮光線條件下的影像飽和度,並降低超低光環境下的雜訊水準。
### Nyxel
OMNIVISION 的 Nyxel 近紅外線成像技術,是為了滿足先進的機器視覺、監控和汽車攝影機應用的低光和夜視效能要求而開發,結合了厚晶片像素架構和對晶圓表面紋理的精心管理以提高量子效率。此外,擴展的深溝隔離有助於在不影響感測器暗電流的情況下,保留調製轉換函數,進一步提高夜視能力。效能改進包括影像品質、擴展的影像偵測範圍和更低的光源要求,從而降低整體系統功耗。
### Nyxel 2 | [
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豪威科技 | 第二代 Nyxel 近紅外技術在第一代基礎上改進,增加矽的厚度以提高成像靈敏度,深溝隔離得到進一步擴展以解決串擾問題,而不影響光學調節傳送功能。晶片表面經過改進後,改善擴展的光子路徑並增加光電子轉換,與第一代技術相比,該感測器在不可見的 940 奈米電磁波譜中,達成了 25% 的改進,在幾乎不可見的 850 奈米近紅外波長中,達成了 17% 的改進。
### LED 閃爍緩解和高動態範圍
高動態範圍成像依賴於演算法,將數個影像擷取合併為一個,以創建一個比單獨的原始擷取更高品質的影像。發光二極體(LED)照明在 HDR 下可能會產生閃爍效應。這對機器視覺系統來說是個問題,例如用於自動駕駛汽車的機器視覺系統。這是因為 LED 在汽車環境中無處不在,從車頭燈到交通號誌、路標等都使用 LED 燈具。雖然人眼可以適應 LED 的閃爍,但機器視覺卻不能。為了減輕這種影響,OMNIVISION 採用了分割像素技術。讓一個大的光電二極體使用短曝光時間捕捉一個場景。一個小型光電二極體則使用長曝光時間同時捕捉 LED 信號。然後,這兩幅影像會被整合到最終的圖片中,成為一個無閃爍的影像。
## 產品
### CMOS 影像感測器
OMNIVISION CMOS 影像感測器的解析度範圍涵蓋 6400 萬像素到 100 萬像素以下。2009 年,OMNIVISION 收到了來自蘋果公司 320 萬像素和 500 萬像素(CMOS image sensor,CIS)的訂單。
### ASICS
OMNIVISION 生產特殊應用積體電路(ASIC),作為其影像感測器的配套產品,用於汽車、醫療、擴增實境和虛擬實境(AR/VR)以及物聯網應用。
### CameraCubeChip
OMNIVISION 公司的 CameraCubeChip,是一個完全封裝的晶圓級相機模組,尺寸為 0.65 毫米 X 0.65 毫米,可整合到直徑小至 1.0 毫米的一次性內視鏡和導管中,這些醫療裝置應用於從診斷到微創手術在內的一系列醫療程式。
### LCOS
OMNIVISION 生產用於顯示應用的液晶覆矽(LCOS)投影技術。
2018 年,AR 新創公司 Magic Leap 在其 Magic Leap One 混合實境產品中,同時採用了 OMNIVISION LCOS 技術和感測器橋接 ASIC。
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豪威科技 | 數位影像市場已經匯聚成兩個主要的發展方向:數位攝影和機器視覺。雖然智慧型手機的相機曾有一段時間為推動市場的主要動力,但自 2017 年以來,機器視覺應用推動了新的發展,自動駕駛汽車、醫療設備、小型化保全攝影機和物聯網(IoT)裝置都依賴於先進的影像技術。
OMNIVISION 廣泛的類比產品包括電源管理裝置,如 LED 驅動器、DC-DC 開關和線性穩壓器、電壓基準,以及特殊功能裝置,如 USB 電源開關、負載開關和介面裝置。獨立產品則包括 ESD/TVS、MOSFET、絕緣柵雙極電晶體和蕭特基二極體。
OMNIVISION 的觸控和顯示驅動器整合(TDDI)產品包括 LCD TDDI、OLED DDIC 以及用於行動、PC 和汽車應用的獨立觸控解決方案。
OMNIVISION 產品為以下市場區隔所設計:
* 行動裝置
* 汽車
* 安全
* 物聯網 / 新興應用
* 運算
* 醫療
以下是已被終端用戶採用的 OMNIVISION 產品之範例:
* 蘋果公司 iPhone 5 的前置相機鏡頭是 OV2C3B。
* 2013 年發佈的樹莓派官方 500 萬像素相機鏡頭使用的是 OV5647。
* 2014 年,谷歌為將 AR/VR 技術導入行動應用,開發了 3D 地圖技術 Project Tango。Tango 包含一些 OMNIVISION 的產品,包括一個可實現高解析度照片和影片的 400 萬像素 RGB-Ir 感測器、其標準鏡頭中的深度感知,以及一個低功耗的 CameraChip。
* Netgear 公司的 Arlo 家庭保全攝影機是一個電池操作的無線攝影保全系統,其包含多款 OMNIVISION 產品,包括 OV00788 作為攝影機的影像訊號處理器,以及 OV9712,後者為一個具有影片擷取能力的 100 萬像素逐行掃描 CMOS 影像感測器。
* Ring 門鈴使用一個高傳真相機,其中包含一個 OMNIVISION OV9712 100 萬像素影像感測器 OMNIVISION H.264 和一個用於影片處理的影片壓縮晶片。
* 索尼 PlayStation 在 PlayStation\_Camera 中使用了兩個 OV9713 CMOS 影像感測器,以及兩個 USB 橋接 ASIC 解決方案。此外,其搭載了一個專門為索尼製造的 OV580 ASIC 晶片。 | [
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豪威科技 | * 汽車系統供應商 ZF Group 在其第四代 S-Cam 中納入了 OMNIVISION CMOS 影像感測器,包括單鏡頭和三鏡頭的設定。
* 截至 2020 年 6 月為止,特斯拉 Model S/X/3/Y 的車尾自動駕駛鏡頭使用了 OV10635 720p CMOS 感測器。
* 華碩 ZenFone 4 智慧型手機系列的所有五個型號都包括雙鏡頭設定,中端機型的前置鏡頭和輔助感測器均使用 800 萬像素的 OV8856,以提供 120 度的超寬視角。ZenFone 4 Selfie 使用 500 萬像素的低解析度 OV5670 作為其副感測器,目的同樣是為了獲得超寬視角。
* 微軟 Surface\_Pro\_4 配備了一個 800 萬像素的後置鏡頭,採用 OV5693 影像感測器,以及一個 500 萬像素的前置鏡頭,採用 OV8865 影像感測器。後置鏡頭有 1.4 微米的像素,和適用於低光照情況的 F/2 光圈,前置鏡頭則提供了更寬的視角,用於視訊通話,畫質帶有些許顆粒感。
* 高通虛擬實境設計套組(Virtual Reality Design Kit,VRDK)的開發,是為了給消費電子製造商提供基礎,以便它們能夠在高通驍龍 VR 硬體基礎上,開發 VR 頭戴式裝置。為實現定位追蹤,該公司設計了由 OV9282 全局快門影像感測器支援的板載相機,可以用 120Hz 的速度擷取 1280 x 800 影像,或以 180 赫茲的速度擷取 640x480 像素影像。高通選擇該款產品的理由,是因低延遲使其成為 VR 頭戴式裝置的理想選擇。
* 戴爾的 Latitude 5000、7000 和 9000 系列筆記型電腦採用了 OMNIVISION 的 OV02C 影像感測器。
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解码宇宙 | **解碼宇宙:新信息科學看天地萬物**(英語:_Decoding the Universe: How the New Science of Information Is Explaining Everything in the Cosmos, from Our Brains to Black Holes_)是美國作家查爾斯・塞費 2007 年出版的一本關於資訊理論的書籍,是他的第三部科普作品。
## 梗概
本書圍繞資訊理論展開,討論了其中的許多問題,如退相干與概率、相對論與量子力學,特別是艾倫・圖靈和埃爾溫・薛丁格的工作。
## 參考資料
## 外部連結
官方網站 | [
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] |
灵异数据 | **幽靈數據**(英語:Ghost data), 是指從數據科學、統計學角度處理我們一般看不見的數據,量子成像或幽靈成像,「暗物質」或「暗能量」及其在計算機視覺領域中的新發現,甚至還包括與文物資料、經歷等相關的認知數據。
在量子場論的術語中,幽靈(ghost)、幽靈場(ghost field)或規範幽靈(gauge ghost)是規範場論中的非物理狀態。在局部場超過多個物理自由度的情況下,必須使幽靈保持理論的不變性。在數據科學、統計學、計算機等術語中,幽靈數據包括為數字幽靈 (digital ghost), 虛擬數據(如仿真數據、虛擬病人)、缺失數據、偽造數據、高度稀疏數據,及其他類似數據。令人容易聯想到的是缺失數據。由於缺失機制(可忽略或不可忽略、隨機缺失或非隨機缺失等)的不同,處理方法也不盡相同。除了缺失數據,幽靈數據還包括其他看不見的數據。這些數據可能是因為部分人員能夠感知而其他人不能感知的數據。
## 概述
幽靈數據由 John Sall 和 Dennis Lin 教授率先在系列邀請報告中闡述。幽靈數據廣泛存在於各種歷史記錄的數據中,包括記錄的日記、照片、錄音、視頻,甚至存儲在化石和文物等中的記憶信息。儘管這些文物僅記錄部分表面特徵,但是一部分人能感知其相關的更多的信息,而其他人不能感知到那些信息。能夠感知更多信息的人就能構建部分並近似複製其整個生活過程。例如,在文物虛擬修復方面,數據科學家與文物專家的合作,能夠能更多地存儲其記錄,並還原它們所攜帶的記憶信息。隨著技術的進步,將能為原始生活提供完美複製品。
## 數據類型
幽靈數據常包括幽靈成像、虛擬數據、缺失數據、偽造數據、仿真數據、「暗物質」、高度稀疏數據,及其他類似數據。令人容易聯想到的是缺失數據。由於缺失機制的不同,處理方法也不盡相同。數據缺失可以分為隨機缺失 (missing at random, MAR) 和非隨機缺失(Missing not at random, MNAR)。缺失數據處理方法主要包括使用樣本抽樣推斷、貝葉斯推斷和似然法推斷等。對於實驗設計,隨機完全區塊設計也會遇到缺失問題。不完整均衡區塊設計也可被當成隨機完全區塊設計帶有缺失數據進行統計分析。
## 相關條目
* 大數據
* 幽靈數據
* 數據科學
* 缺失數據
* 量子成像
* 暗物質
* 虛數
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陣發混沌 | **陣發混沌**(intermittency)是動力系統的名詞,是指系統不規則地出現似乎週期性的行為以及混沌行為的情形(泊姆–曼內維爾情境),或是在二種不同的混沌行為之間切換的情形(危機引發的陣發混沌,crisis-induced intermittency) 。
Pomeau 和 Manneville 曾敘述過三種幾乎週期性的系統出現陣發混沌的情形,其狀態空間中,會有不規則地出現混沌的區域。第一類、第二類及第三類分別對應鞍結點分岔、次臨界的霍普夫分岔、以及反向的倍周期分岔。這些看似週期性的運動,其實只是近似週期性,會慢慢的從不穩定的周期點中漂離。最終系統會偏離周期點,開始出現混沌的行為,一直到系統足夠接近周期點為止,又會恢復看似週期性的運動。系統維持在看似週期性運動的時間會靈敏的受到許多因素影響,因此無法預測會持續的時間。
另一種陣發混沌,稱為開關式的陣發混沌(on-off intermittency),是之前橫向穩定,但維度小於嵌入空間的混沌吸引子開始由穩定變不穩定所出現的現象。吸引子軌道內的不穩定軌道會使系統推到鄰近的空間中,在回到吸引子軌道之前會有暫時性的爆發。
危機引發的陣發混沌(crisis-induced intermittency)是指混沌吸引子遇到動態系統中稱為「危機」(Crisis)的現象,有二個或多個吸引子的吸引力盆地(basin of attraction)互相重疊,因此在第一個吸引子上的軌道可能會進入第二個吸引子的吸引力盆地,受第二個吸引子吸引,直到又再進入第一個吸引子的吸引力盆地為止。
陣發混沌常見於湍流流場,或是即將變成湍流的流場。在高度湍流的流場中,陣發混沌會以不規則的耗散動能,以及速度變化量的異常比例來表示。在湍流噴射流或是其他沒有剪力的湍流中,也會出現湍流和非湍流不規則交替出現的情形。在管流及其他有封閉截面的剪力流中,在從層流進展到湍流時,也會有陣發混沌的抽吸情形。在振盪器電路以及化學反應中,也可以看到陣發混沌的行為。
## 相關條目
* 泊姆–曼內維爾動力學
* 危機 (動態系統)
* 湍流
* 間歇熒光:有機分子以及膠體量子點(奈米晶體)的閃爍
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陣發混沌 | * Staicu, A. D. Intermittency in Turbulence (PDF). Eindhoven University of Technology. 2002 [2020-08-20]. (原始內容存檔 (PDF) 於 2014-03-27).
* Vassilicos, J. C. Intermittency in turbulent flows. Cambridge University Press. 2000: 288. Bibcode:2000itf..book.....V. ISBN 0-521-79221-5.
## 外部連結
* Transition to chaos through intermittency (頁面存檔備份,存於網際網路檔案館) | [
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通用近似定理 | 在人工神經網絡的數學理論中, **通用近似定理**(或稱**萬能近似定理**)指出人工神經網路近似任意函數的能力。 通常此定理所指的神經網路爲前饋神經網路,並且被近似的目標函數通常爲輸入輸出都在歐幾里得空間的連續函數。但亦有研究將此定理擴展至其他類型的神經網路,如卷積神經網路、放射狀基底函數網路、或其他特殊神經網路。
此定理意味著神經網路可以用來近似任意的復雜函數,並且可以達到任意近似精準度。但它並沒有說明要如何選擇神經網絡參數(權重、神經元數量、神經層層數等等)來達到想近似的目標函數。
## 歷史
### 1900 年代
### 1950 年代至 60 年代
Kolmogorov 與學生 Arnold 在 1950 年代及 60 年代期間,證明多元函數可分解為以下形式(e.g. Kolmogorov–Arnold 表示定理):
: $f(\mathbf {x} )=f(x_{1},\ldots ,x_{n})=\sum _{q=0}^{2n}\Phi _{q}\left(\sum _{p=1}^{n}\phi _{q,p}(x_{p})\right)$ .
### 1980 年代後
喬治・西本科於 1989 年證明了單一隱藏層、任意寬度、並使用 S 型函數作爲激勵函數的前饋神經網路的通用近似定理。科特・霍尼克(英語:Kurt Hornik)在 1991 年證明 ,激勵函數的選擇不是關鍵,前饋神經網路的多層神經層及多神經元架構才是使神經網絡有成為通用逼近器的關鍵。
### 2020 量子計算
量子神經網絡可以用電路量子計算機的不同數學工具來表示,從量子感知器到變分量子電路,都基於量子邏輯閘的組合。變分量子電路基於參數電路,不涉及神經網絡。相反,量子感知器能夠設計具有與前饋神經網絡相同結構的量子神經網絡,前提是每個節點的閾值行為不涉及量子態的崩潰,即沒有測量過程。 2022 年,這種為量子神經網絡提供激活函數行為的免測量構建模塊已經被設計出來 。
量子電路返回與量子比特相關的 -1 到 +1 區間內的壓縮函數的任意近似值。這種設計任意量子激活函數的方法通常可以實現量子多感知器和量子前饋神經網絡。
## 參見
* Kolmogorov–Arnold 表示定理
* 代表定理
* 沒有免費的午餐定理
* Stone–Weierstrass 定理
* 傅立葉級數
* 希爾伯特第十三問題
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電動航天推進 | 電動式推進是指利用電力或磁場作為太空載具的動力。這系統大多採用加速電離子的技術。
比衝越高代表效率越好,亦即可以用相同質量的燃料產生更多的動量。因為電動發動機比化學燃料火箭有更高的排氣速度,所以比化學燃料火箭消耗更少燃料,但由於能源所限,其推力會比化學燃料火箭弱得多。雖然電動推進器的推力較少,但推力卻可維持一段很長的時間。經過長時間後,電動發動機能加速到一個相當可觀的速度,因此電動發動機比化學燃料火箭更適合於深太空任務。
目前,電動式推進發展已相當成熟,已廣泛應用於各種太空任務上。俄羅斯的衛星已經採用電動推進有幾十年,預計到 2020 年,一半的新型衛星將完全採用電動式推進。到 2019 年,在太陽系運行的 500 多個太空載具將採用電動推進系統。其系統除了作為它們的主要動力外,亦會用作固定太空載具在軌道上及軌道提升等功能。而日後所發展出電動發動機更可產生每秒 100 公里的速度增量(Δv)。雖然這速度能使太空載具(且是核能驅動)前往至太陽系外圍的星球,卻還不足以進行星際間的穿梭。理論上,電動式推進如能搭配外部能源(透過雷射方式傳送動力)運作,是有可能進行星際穿梭。由於電動式推進產生的推力不夠強,所以並不適合用於火箭從地球發射上太空的過程。
## 驅動形式
### 離子和電漿推進
此一形式的發動機利用噴出離子作為動力來源。有別於一般火箭發動機,由於並不需要噴嘴,所以並不被視為真正的火箭發動機。離子發動機基本上等同於粒子加速器,原理是將離子從排氣口噴射出去以產生動力。目前知名的粒子加速器並非用作推進器,主要是用在研究及工業上,為科學測量及核散裂反應 (nuclear spallation) 或離子注入 (ion implantation) 等研究作出貢獻,如歐洲核子研究中心使用大型強子對撞機進行的基礎物理研究。
根據用於加速離子的作用力種類,太空載具所使用的電動推進器可分為三種:
#### 靜電式推進
任何裝置藉庫侖靜電力產生加速度作為動力,皆屬於靜電式推進,包括:
* 網格離子推進器 Gridded ion thruster
* 國家國家航空暨太空總署太陽能技術應用設備 NASA Solar Technology Application Readiness (NSTAR)
* 高能量電力推進 High Power Electric Propulsion (HiPEP) | [
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電動航天推進 | * 射頻離子推進器 Radiofrequency ion thruster
* 霍爾推進器 Hall Effect Thruster (HET)
* 固定電漿推進器 Stationary Plasma Thruster (SPT)
* 陽極層離子推進器 Thruster with Anode Layer (TAL)
* 離子膠體推進器 Colloid Ion Thruster
* 場致發射電力推進 Field Emission Electric Propulsion (FEEP)
* 奈米粒子場提取推進器 Nano-particle field extraction thruster
##### 電熱式推進
電熱式推進指儀器透過產生電漿令推進劑加熱,並通過實體噴嘴或磁場噴嘴,將推進劑的熱能轉化為動能。通常採用低分子量氣體 (如氫、氦及氨) 作為推進劑。
電熱式發動機通過噴嘴將熱能轉化為分子的直線運動,以成為自身動力,可視它為火箭。
雖然電熱式發動機在比衝 (ISP) 方面的表現並沒有特別突出 (500 到 1000 秒),仍比冷氣體推進器、單基發動機及大部份的雙基發動機優秀。蘇聯曾於 1971 年起採用電熱式發動機,包括蘇聯製的「Meteor-3」、「Meteor-Priroda」、「Resurs-O」系列的衛星,以及俄製的「Elektro」衛星。目前洛克希德・馬丁 (Lockheed Martin) 的 A2100 衛星正採用由洛克達因公司 (Aerojet) 製造的電熱系統 MR-510,並以聯胺作為推進劑。電熱式推進器包括:
* 電弧噴射發動機 Arcjet Thruster
* 電阻加熱電漿發動機 Resistojet Thruster
* 可變比衝磁電漿火箭 Variable Specific Impulse Magnetoplasma Rocket (VASIMR)
##### 電磁式推進
電磁式推進指儀器利用離子加速,即離子受到勞侖茲力或電磁場作用 (其電場與離子加速的方向不相同) 影響,作為飛船動力。電磁式推進器包括:
* 無電極電漿推進器 Electrodeless plasma thruster
* 磁電漿動力推進器 Magnetoplasmadynamic thruster
* 脈衝感應推進器 Pulsed inductive thruster
* 脈衝電漿推進器 Pulsed plasma thruster | [
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電動航天推進 | * 螺旋雙層結構推進器 Helicon Double Layer Thruster
### 非離子式推進
##### 光子式推進
光子推進器意指儀器透過發射光子產生推力。詳見以下頁面:
* 雷射推進 Laser propulsion
* 光子火箭 Photon rocket
##### 電動纜索式推進
電動纜索是一條很長的導線。如將一條纜索連接上一個特定的衛星,它就能以發電機的電動原理運作,將動能轉化為電動,或以發電機的原理運作,將電動轉化為動能。當纜索在地球的磁場中移動,便能產生電勢。電動纜索採用甚麼種類的金屬導線取決多個因素,主要包括其導電性及低密度性。次要因素則是金屬的價格、強度及熔點。詳見以下頁面:
* 電動纜索 Electrodynamic tether
##### 其他具爭議性的推進形式
除上述的非離子式驅動形式外,還有數個推進方式曾經被提出,但尚未清楚這些方法能否在現今所知的物理規則下實現,包括:
* 量子真空電漿推進器 Quantum Vacuum Plasma Thruster
* 射頻共振空腔推進器 RF resonant cavity thruster
### 穩定輸出型及非穩定輸出型
電動推進系統亦可以分類為穩定輸出型 (能於指定時間內持續地產生動力) 及非穩定輸出型 (以脈衝方式噴射達到預期推力)。事實上,這分類方式不只可應用在電動推進系統上,亦可以應用在任何推進形式的引擎上。
## 動力特性
由於電動式發動機的動力相當有限,因此產生的推力比化學燃料發動機更少,其推力差距甚至高達好幾個數量級。並且化學燃料火箭產生動力的方式快而直接,電動系統卻需要多個程序才能產生動力。然而在同等的推力下,電動式推進能以較少燃料,為太空載具帶來可觀的航行速度,這一點相對化學燃料發動機佔有極大優勢。化學燃料發動機只能於很短的時間內運作,並大多只會於慣性軌道 (inertial trajectory) 上航行。當接近行星時,電動火箭雖然沒法提供足夠的推力使飛船脫離星球的表面,但長時間性的低推力卻可以令飛船在星球附近的地方航行。
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福格特滤波器 | **原子線濾波器**是物理科學中用於過濾電磁輻射的高效光學帶通濾波器,工作過程精準,而且信號損失極小。原子線濾波器的工作原理是吸收或共振原子蒸氣光譜線,所以也稱**原子共振濾波器**。
原子線濾波器主要分三大類:**吸收-再發射原子線濾波器**、**法拉第濾波器**,以及**福格特濾波器**。吸收-再發射濾波器的面世時間最早,所以通常簡稱「原子線濾波器」,另外兩種大多採用全稱「法拉第濾波器」和「福格特濾波器」。原子線濾波器可以根據不同需求採用不同設計和工作機制,但基本策略相同:利用金屬蒸氣狹窄的吸收譜線或共振譜線來過濾光,除特定頻率能通過外,其他光線都被阻擋。
原子線濾波器在光學上可以起到鎖相放大器的作用,通常在需要有效檢測窄帶信號(幾乎都是雷射)的科學應用中使用,如果沒有這樣的設備,窄帶信號就會被日光之類寬帶信息源遮擋。除光學雷達經常使用外,人們還在研究原子線濾波器對雷射通訊系統的潛在用途。與干擾濾波器和利奧濾光器之類常規電介質濾光器相比,原子線濾波器效果最為理想,但因結構更加複雜導致只能在抑制背景的檢測環境中使用,實現抑制強烈背景信息源,檢測弱信號的目的。與同屬高端濾光器的法布里-珀羅干涉儀相比,法拉第濾波器更加堅固耐用,而且 1.5 萬美元的單價只有前者六分之一。
## 歷史
原子線濾波器的前身是 20 世紀 50 年代尼古拉斯・布隆伯根設計的紅外量子計數器,是根據約瑟夫・韋伯(Joseph Weber)理論設計的量子力學放大器,能以極小噪音檢測紅外線輻射。X 射線和伽馬射線放大器實現零自發輻射後,韋伯認為可以將技術應用到紅外光譜。布隆伯根詳細描述這種設備,並稱為「紅外量子計數器」。
無論 X 射線放大器、伽馬射線放大器還是紅外量子計數器,使用的介質都是晶體和過渡金屬離子雜質,吸收低能量光並重新發射成可見光。到 20 世紀 70 年代,人類又在「原子蒸氣量子計數器」中使用原子蒸氣檢測紅外電磁輻射,因為這種方式比之前使用金屬鹽和晶體效果更好。 | [
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福格特滤波器 | 接下來,科學家利用紅外線放大器的基本工作原理開發被動鈉原子線濾波器。這種設計及緊隨其後的設計尚欠成熟,量子效率都很低,響應速度慢。由於這便是原子線濾波器的原始設計,許多文獻便專門用「原子線濾波器」代指吸收-再發射原子線濾波器。1977 年,傑里・吉爾布瓦克斯(Jerry A. Gelbwachs)、克里斯多福・克萊因(Christopher F. Klein)和約翰・韋塞爾(John E. Wessel)制出第一台主動原子線濾波器。
法拉第濾波器在 1978 年前面世,與當時的吸收-再發射原子線濾波器相比「進步顯著」。1992 年 8 月 26 日,詹姆斯・H・門德斯(James H. Menders)和埃里克・科雷瓦(Eric J. Korevaar)獲得福格特濾波器專利,比之前兩種濾波器更先進。福格特濾波器更加緊湊,「很容易設計成與永磁體一起使用」。1996 年,法拉第濾波器已開始結合光學雷達使用。
## 特徵
原子線濾波器的技術定義是「超窄帶、大接收角的各向同性濾光器」,其中「超窄帶」指能夠通過設備的狹窄頻率範圍,原子線濾波器的通頻帶大多在 0.001 奈米量級。大接收角指設備的接收角很大(接近 180°),是原子線濾波器的重要參數;光線以一定角度射入基於反射層和折射層間距工作的傳統電介質濾光器時,有效間隔會發生變化。
濾波器的確切參數(溫度、磁場強度、波長等)能按具體需要調整。由於系統結構極其複雜,各項參數需用計算機計算。
### 輸入 / 輸出
原子線濾波器能在電磁波譜的紫外線、可見光和紅外線頻率範圍工作。吸收-再發射原子線濾波器工作時必須改變光線頻率,被動設備還需轉至低頻(即紅移)來節約能源,這也導致被動設備通常無法在紅外線頻率工作,因為輸出頻率太低,已經沒有意義。如果配合光電倍增管,那麼「原子共振濾波器的輸出波長應該能夠保持在特定光譜區,確保商用、大範圍、長壽命的光電倍增管能保持最高靈敏度」。這類應用下,主動原子線濾波器功能更便捷,比被動原子線濾波器更具優勢,「產生接近紫外線的輸出波長,這樣的光譜區能讓功能完善的光電倍增管保持最高靈敏度」。
被動原子線濾波器的輸入頻率幾乎必須完全對應蒸氣室的自然吸收光譜線,主動原子線濾波器遠比被動設備靈活,但激發的蒸氣會促使設備吸收其他頻率的光。
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福格特滤波器 | 吸收-再發射原子線濾波器的響應時間直接影響光源向接收器傳送信息的速率,所以最小響應時間是這類原子線濾波器的重要特徵。吸收-再發射原子線濾波器的響應時間很大程度上取決於蒸氣室內已激發原子的自發衰減。傑里・蓋布瓦克斯曾於 1988 年記載:「通常快速自發發射時間約為 30 奈秒,說明信息傳送速率上限約為 30 兆赫茲。」
人類想方設法縮短原子線濾波器的響應時間。20 世紀 80 年代後期,人們已經開始用某些氣體來催化蒸氣室電子衰減。1989 年,埃里克・科雷瓦(Eric Korevaar)設計出「快速原子線濾波器」,能在沒有感光板的情況下檢測發出的螢光。憑藉這些手段,人類已經輕易達到千兆赫茲的傳輸效率。
### 效用
#### 效率
原子線濾波器本質上是非常高效的濾光器,通常屬「超高品質」類,品質因子在 105 到 106 範圍。這一定程度上是因為「交叉偏振片…… 能夠以優於 10−5 的抑制比阻擋背景光」。法拉第濾波器的通頻帶通常為數 GHz,總輸出可能在總輸入光強度的一半左右。光損耗由不夠完善的透鏡、濾鏡和窗口反射或吸收。
#### 帶通
原子線濾波器帶通一般和蒸氣室都卜勒輪廓相等,頻率就在純光源能激發蒸氣室的自然範圍。都卜勒輪廓指蒸氣室因分子運動影響發射的都卜勒頻移輻射光譜寬度,該數值在原子偏大、溫度偏低時偏小,這樣的系統更為理想。
部分因素會導致實際情況與上述不符,如果能確保傳送光譜寬帶大於都卜勒增寬效果就更理想。以追蹤快速加速的目標為例,原子線濾波器的帶通必須在反射光最大和最小值範圍內。目前公認的帶通提升法是向蒸氣室輸入惰性氣體,這樣不但能加寬光譜線,還能提升濾波器傳送效率。
#### 噪音源
原子線濾波器雖然效率很高,但還遠非完美,存在許多會導致錯誤(又稱「噪音」)的問題,例如與濾波器工作過程和信號光源強度無關的電磁輻射。原子線濾波器本身及其內部的熱輻射產生噪音,部分熱輻射直接由濾波器產生,而且正好在第二道寬帶濾光器的帶通範圍內。如果濾波器的輸出設定在紅外線範圍,就會因為絕大多數熱輻射都在紅外光譜範圍內而出現更多噪音。這些熱輻射可能會激發蒸氣,還可能產生設備用來檢測的輻射。
主動原子線濾波器沒有「狀態選擇」功能,所以比被動設備更容易產生噪音,持續的輸入可能意外激發錯誤光線擊中的原子直達能量臨界點,進而自發發出輻射。 | [
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福格特滤波器 | 原子吸收或共振線激發非目標波長,也會產生噪音,雖然多數「附近」躍遷產生的波長至少距目標十奈米,寬帶濾波器足以阻擋,但目標吸收線的精細和超精細結構可能吸收不正確的光譜頻率,然後傳遞至輸出傳感器。
#### 關聯現象
輻射俘獲效應可能嚴重影響原子線濾波器性能,所以需要調整設備。20 世紀 70 年代至 80 年代初,人類利用原子線濾波器開展的原始研究嚴重高估信號帶寬。研究、分析輻射俘獲效應並優化設備後,情況顯著改觀。
蒸氣室共振線的位置和寬帶是所有原子線濾波器最重要的特徵。受斯塔克效應和塞曼分裂影響,基準吸收線可能「分裂」至更細,「可以利用這種效果來調諧檢測器。」因此,操縱電場和磁場可能會改變濾波器的其他特徵(即造成帶通變更)。
## 類型
### 吸收-再發射原子線濾波器
吸收-再發射原子線濾波器吸收所需波長的光後發射能繞過寬帶濾光鏡的光,其中被動機型用高通濾波器阻擋所有低能量入射光,蒸氣室吸收的信號與蒸氣中的極細吸收線重合,室內原子隨即激發。接下來蒸氣室經過更低頻率的螢光再發射光信號。另外還有低通濾波器阻擋高於螢光頻率的輻射。主動機型利用光泵和電泵作用激發原子吸收或發射不同波長的光。主動原子線濾波器可能需要其他傳統濾光器系統配合。
### 法拉第濾波器
法拉第濾波器又名磁光濾波器、法拉第色散濾光器或激發法拉第色散濾光器,工作原理是用蒸氣室旋轉光的偏振。這種旋轉是因法拉第效應和異常色散效應,在原子吸收線附近發生,只旋轉具有蒸氣室共振頻率的光,而其他頻率的電磁輻射則由偏振板阻擋。這種現象與塞曼效應(即原子吸收線在有磁場存在時會發生分裂)有關並受其影響增強。
目標輻射偏振的旋轉角與多個因素緊密相關,如磁場強度 $B$ 、蒸氣室寬度 $d$ 、室內蒸氣的韋爾代常數 ${\mathcal {V}}$ (由蒸氣室溫度、光線波長決定,有時還受磁場強度影響)。關係方程如下:
: $\beta ={\mathcal {V}}Bd$
### 福格特濾波器
福格特濾波器是在法拉第濾波器的基礎上把磁場偏移至與光方向垂直,而與偏振片的偏振成 45° 角。福格特濾波器中的蒸氣室相當於半波片,在福格特效應影響下把偏振延緩 180°。
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福格特滤波器 | 光線通過原子線濾波器前可能需要經過準直儀,用於矯直入射光線,確保光線接下來能夠通過濾波器的其他部分,但部分情況下也可能不需要準直儀。準直儀後的高通濾波器能阻擋近波長太長的入射光,約占到全部入射光的一半。法拉第和福格特濾波器則用第一塊偏振片阻擋不符要求的入射光。
出於實用角度考慮,人們還將其他系統結合原子線濾波器的其餘部分使用。例如,法拉第濾波器使用的偏光片實際上已經不會阻擋大部分輻射,「因為這些偏光片只能在有限的波長範圍內工作……(所以將)寬帶干擾濾波器和法拉第濾波器結合使用」。干擾濾波器的帶通可以達到實際濾光器的兩百倍。光電倍增管也經常用於將輸出信號強度提升到可用水平。雪崩光電二級管效率更高,能夠取代光電倍增管使用。
### 蒸氣室
雖然每種原子線濾波器的工作原理不盡相同,但配備的蒸氣室都很相似。濾波器蒸氣室的熱力學特徵與設備品質休戚與共,所以受到嚴格控制(如確保磁場的必要強度)。光線通過氟化鎂之類材料製成的低反向窗口進出蒸氣室,蒸氣室的其他各面可以用任何不透明的材料,但考慮到蒸氣室的溫度通常超過 100°C,所用的不透明材料一般是耐熱金屬或陶瓷。
原子線濾波器需要很高的蒸氣室氣壓,所以大部分蒸氣源是鹼金屬,許多鹼金屬還擁有所需光譜的吸收線和共振頻率。常見的蒸氣源金屬包括鈉、鉀和銫,還可能用到氖這樣的非金屬蒸氣。早期的量子計數器使用晶體中的固態金屬離子,這樣的材料應該也能在各種現代原子線濾波器上使用,但估計是因原子蒸氣效果更好,還沒有人嘗試使用晶體。
## 應用領域
原子線濾波器能夠有效濾除日光,識別微弱的窄帶信號,所以在光學雷達與其他雷射跟蹤和檢測應用中最為常見。這種設備還能用於過濾地球的熱背景,檢測抗生素藥效或充當通用過濾器。
### 雷射跟蹤與通訊
如果沒有原子線濾波器,雷射跟蹤與通訊可能非常困難。增強型感光耦合元件相機必須結合簡單的電介質濾光器(如干擾濾波器)來遠程檢測雷射發射。增強型感光耦合元件的效率不足,而且必須結合可見光譜範圍內的脈衝雷射傳輸。藉助原子線濾波器的優異過濾系統,普通感光耦合元件都能使用更有效率的連續波雷射。人類已經制出帶通約為 0.001 奈米的原子線濾波器,改善經過傳統過濾後雷射接收器的背景抑制。新系統總能耗僅為老版本的三十到三十五分之一,所以人們已經提出並開發結合原子線濾波器並支持空基、水下通訊的敏捷雷射通訊應用。
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福格特滤波器 | 光學雷達向大氣的相應位置發射雷射,然後分析反向散射回來雷射束的都卜勒頻移,目標區域的風速、風向可能也要計算。由此可以研究熱結構、中間層的季節變化,以及晝夜或半日周期的潮汐規律。這些信息對氣象學和氣候學舉足輕重。
如果無法有效追蹤微弱的雷射信號,每天大氣數據的收集就只能局限在太陽電磁輻射尚未淹沒雷射信號之時。在光學雷達上增加原子線濾波器能有效濾除干擾,確保任何時間都能收集數據。人類已經使用法拉第濾波器配合光學雷達超過十年,科學家在此期間對地球中層大氣的了解遠超原子線濾波器發明以前。
## 參見
* 受激發射
* 夫朗和斐譜線
* 瑞利散射
## 腳註
## 參考文獻
## 專利
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单色仪 | **單色器**是一種光學設備,可機械地從輸入的較寬波長範圍的光或其他輻射中選擇性透射較窄的波長範圍的輻射。
## 用途
可以產生單色光的設備在科學和光學方面都有許多用途,因為材料的許多光學特性都取決于波長。儘管有許多有用的方法來選擇窄帶波長(在可見光範圍內被視為純色),但沒有很多其他方法可以輕鬆地從寬範圍內選擇任意波長帶。有關單色器某些用途的討論,請參見下文。
在硬 X 射線和中子光學中,晶體單色器用於定義儀器的波況。
## 原理
單色儀可以使用稜鏡中的色散現象,也可以使用衍射光柵的衍射現象在空間上分離光的顏色。單色器通常具有將所選顏色引導到出射口的機制。通常,光柵或稜鏡的作用機制是反射。反射稜鏡是通過製作一個直角三角形稜鏡(通常是等邊稜鏡的一半)並將一面磨成鏡面而製成的。光通過斜邊面入射並反射回去,在同樣的表面上折射兩次。總折射和總色散與在透射模式下使用等邊稜鏡時的情況相同。
## 應用
單色器用於許多光學測量儀器以及需要可調單色光的其他機器中。有時,單色光直接對準樣品,然後測量反射或透射光。有時,白光會直接對準樣品,而單色器則用於分析反射或透射的光。在許多螢光計中使用了兩個單色器,一個單色器用於選擇激發波長,第二個單色器用於分析發射的光。
自動掃描光譜儀包括改變由單色器選擇的波長並記錄所測量的量隨波長變化的結果的機制。
如果將成像設備替換出口狹縫,即為光譜儀的基本配置。這種配置允許同時分析多種顏色的色彩強度。可以使用攝影膠片或光電探測器陣列來收集光。這種儀器無需機械掃描即可記錄光譜函數,儘管在解析度或靈敏度等方面可能會打折扣。
吸收分光光度計測量樣品對光的吸收與波長的關係。有時結果表示為透射比,有時則表示為透射比的負對數。比爾 - 朗伯定律將光的吸收與吸光物質的濃度,光程長度以及材料的固有特性(稱為摩爾吸光係數)聯繫起來。根據這種關係,強度的降低與吸收物質濃度和光程長度呈指數關係。使用透射比的負對數時,其減少是線性的。此值的舊命名法是光密度(OD),當前命名法是單位吸光度(AU)。一個 AU 是光強度降低十倍。六個 AU 減少了一百萬倍。
吸收分光光度計通常包含一個單色器,以向樣品提供光。一些吸收分光光度計具有自動光譜分析功能。 | [
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单色仪 | 吸收分光光度計在化學,生物化學和生物學中有許多日常用途。例如,其被用於測量許多吸收光的物質的濃度或濃度變化。許多生物材料(如酶)被用於測量的的關鍵特徵是通過啟動化學反應,這些化學反應會產生顏色變化,取決於所研究材料的存在或活性。光學溫度計是通過校準材料的吸光度隨溫度的變化而創建的。此外還有許多應用。
分光光度計用於測量鏡子的鏡面反射率和有色物體的漫反射率。它們用於表徵太陽鏡,雷射防護眼鏡和其他光學濾鏡的性能。
在紫外線,可見光和近紅外光中,吸收率和反射率分光光度計通常用單色光照射樣品。在相應的紅外儀器中,單色器通常用於分析來自樣品的光。
單色器還用於光學儀器中,該儀器可測量除簡單吸收或反射以外的其他現象,無論光的顏色如何變化很大。圓二色光譜儀例如包含單色儀。
雷射產生的光比此處討論的光學單色儀的單色要多得多,但是只有一些雷射很容易調諧,並且這些雷射的使用並不簡單。
單色光允許測量成像設備(例如 CCD 或 CMOS 成像器)的量子效率(QE)。來自出口狹縫的光通過擴散器或積分球傳遞到成像設備,同時經過校準的檢測器同時測量光。成像器,校準檢測器和單色儀的配合使人們可以計算為給定波長 QE 的光子生成的載流子(電子或空穴)。
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] |
算法数论 | 在數學和計算機科學領域中,**計算數論**(英語:computational number theory,或稱為**算法數論**(英語:algorithmic number theory),是伴隨著電子計算機的產生而產生的,藉助於高性能計算機的計算能力來研究和解決數論和算術幾何問題,如素數判定、整數分解算法,計算丟番圖方程的解,算術幾何的顯式方法等。它廣泛應用於密碼學,如 RSA 算法,橢圓曲線密碼學,後量子密碼學,並用於研究數論中的猜想和開放性問題,如黎曼猜想,貝赫和斯維訥通 - 戴爾猜想,Abc 猜想,谷山 - 志村猜想,佐藤 - 泰特猜想,朗蘭茲綱領等
## 軟體包
* Magma
* Sage
* Number Theory Library
* PARI/GP
* 快速數論函數庫
## 延伸閱讀
* Eric Bach; Jeffrey Shallit. Algorithmic Number Theory, Volume 1: Efficient Algorithms. MIT Press. 1996 [2020-09-23]. ISBN0-262-02405-5. (原始內容存檔於 2021-09-30).
* David M. Bressoud. Factorisation and Primality Testing. Springer-Verlag. 1989. ISBN 0-387-97040-1. 含有內容需登入查看的頁面 (link)
* Joe P. Buhler; Peter Stevenhagen (編). Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography. MSRI Publications **44**. Cambridge University Press. 2008. ISBN 978-0-521-20833-8. Zbl 1154.11002.
* Henri Cohen. A Course In Computational Algebraic Number Theory. Graduate Texts in Mathematics **138**. Springer-Verlag. 1993. ISBN 0-387-55640-0. doi:10.1007/978-3-662-02945-9. | [
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算法数论 | * Henri Cohen. Advanced Topics in Computational Number Theory. Graduate Texts in Mathematics **193**. Springer-Verlag. 2000. ISBN 0-387-98727-4. doi:10.1007/978-1-4419-8489-0.
* Henri Cohen. Number Theory – Volume I: Tools and Diophantine Equations. Graduate Texts in Mathematics **239**. Springer-Verlag. 2007. ISBN 978-0-387-49922-2. doi:10.1007/978-0-387-49923-9.
* Henri Cohen. Number Theory – Volume II: Analytic and Modern Tools. Graduate Texts in Mathematics **240**. Springer-Verlag. 2007. ISBN 978-0-387-49893-5. doi:10.1007/978-0-387-49894-2.
* Richard Crandall; Carl Pomerance. Prime Numbers: A Computational Perspective. Springer-Verlag. 2001. ISBN 0-387-94777-9. doi:10.1007/978-1-4684-9316-0.
* Hans Riesel. Prime Numbers and Computer Methods for Factorization. Progress in Mathematics **126** second. Birkhäuser. 1994. ISBN 0-8176-3743-5. Zbl 0821.11001.
* Victor Shoup. A Computational Introduction to Number Theory and Algebra. Cambridge University Press. 2012. ISBN 9781139165464. doi:10.1017/CBO9781139165464. | [
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] |
算法数论 | * Samuel S. Wagstaff, Jr. The Joy of Factoring. American Mathematical Society. 2013 [2020-09-23]. ISBN978-1-4704-1048-3. (原始內容存檔於 2020-07-28).
## 參考
## 連結
* 維基共享資源上的相關多媒體資源:Computational number theory | [
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马克斯·普朗克核物理研究所 | **馬克斯・普朗克核物理研究所**(德語:**Max-Planck-Institut für Kernphysik**)是馬克斯・普朗克學會下屬的一所研究機構,位於海德堡,主要從事粒子天體物理學和量子動力學的研究。
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] |
铌酸钾 | **鈮酸鉀** (KNbO3) 是一種無機化合物,化學式 KNbO3。 它是一種無色固體。它被分類為鈣鈦礦結構的鐵電材料。它具有非線性光學特性,並且是某些雷射器的組成部分。 鈮酸鉀的奈米線已用於產生可調諧的相干光。 鈮酸鉀的 LD50 是 3000 mg/kg (大鼠,口服)。
## 晶體結構
在高溫下冷卻後, KNbO3 會經歷一系列的結構相變。 在 435 °C,下鈮酸鉀的結構從立方晶系 (Pm3m) 變成四方晶系 (P4mm)。 進一步冷卻後,在 225°C 時,鈮酸鉀晶體結構從四方(P4mm)變為正交晶系(Amm2)。在 - 50°C 時,晶體結構從正交晶系(Amm2)變為六方晶系(R3m)。
## 在研究中使用
人們已發現鈮酸鉀可用於材料科學研究的許多不同領域, 包括研究雷射的屬性, 量子隱形傳態和研究顆粒複合材料的光學性質。
除了用於電子存儲器之外, 在 IBM 研究院開發的二次諧波產生技術中就使用了鈮酸鉀。 此技術允許小型紅外雷射器將輸出的光轉換為藍光,這是生產藍光雷射器及其相關技術的關鍵技術。
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