열역학적 베테 가설 풀이(thermodynamic Bethe ansatz) - 편집 역사

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2021-02-17T10:30:33Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-28T14:24:46Z

메타데이터: 새 문단

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Pythagoras0: /* 관련된 항목들 */

2013-02-28T21:23:57Z

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2013-02-24T19:06:15Z

@@ 77번째 줄: / 77번째 줄: @@
 [[분류:통계물리]]
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q1366833 Q1366833]

← 이전 판		2020년 12월 28일 (월) 14:24 판
76번째 줄:		76번째 줄:
	[[분류:통계물리]]		[[분류:통계물리]]
	[[분류:통계물리]]		[[분류:통계물리]]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q1366833 Q1366833]

@@ 5번째 줄: / 5번째 줄: @@
 ==basic notions for particle scattering==
-*  infinitely long cylinder of radius <math>R</math><br>
+*  infinitely long cylinder of radius <math>R</math>
-*  N species of particles<br>
+*  N species of particles
-*  mass of particles <math>m_{a}, a=1,\cdots, N</math><br>
+*  mass of particles <math>m_{a}, a=1,\cdots, N</math>
-*  rapidity <math>\theta</math> (also called spectral parameter or wave number)<br>
+*  rapidity <math>\theta</math> (also called spectral parameter or wave number)
-**  a notion from relativity<br>
+**  a notion from relativity
-** http://en.wikipedia.org/wiki/Rapidity<br>
+** http://en.wikipedia.org/wiki/Rapidity
-*  energy <math>E=m_{a}R\cosh \theta</math><br>
+*  energy <math>E=m_{a}R\cosh \theta</math>
-*  momentum <math>p=m_{a}R\sinh \theta</math><br>
+*  momentum <math>p=m_{a}R\sinh \theta</math>
-*  energy-momentum vector <math>p^{\mu}=(E,P)</math><br>
+*  energy-momentum vector <math>p^{\mu}=(E,P)</math>
-*  산란행렬 S-matrix ([[factorizable scattering theory]]):<math>S_{ab}(\theta)</math><br>
+*  산란행렬 S-matrix ([[factorizable scattering theory]]):<math>S_{ab}(\theta)</math>
-*  symmetric matrix kernel :<math>\phi_{ab}(\theta)=-i\frac{d}{d\theta}\log S_{ab}(\theta)</math><br>
+*  symmetric matrix kernel :<math>\phi_{ab}(\theta)=-i\frac{d}{d\theta}\log S_{ab}(\theta)</math>
-*  spectral density of particles <math>\epsilon_{a}(\theta)</math><br>
+*  spectral density of particles <math>\epsilon_{a}(\theta)</math>
-**  also called the pseudoenergy<br>
+**  also called the pseudoenergy
-*  Y-system <math>Y_{a}(\theta)=e^{-\epsilon_{a}(\theta)}</math> i.e. exponential of spectral density<br>
+*  Y-system <math>Y_{a}(\theta)=e^{-\epsilon_{a}(\theta)}</math> i.e. exponential of spectral density
-*  ground state energy <math>E(R)</math><br>
+*  ground state energy <math>E(R)</math>
-*  scaling function <math>c(R)</math> related to the central charge<br>
+*  scaling function <math>c(R)</math> related to the central charge
-*  TBA equation<br>
+*  TBA equation
-**  equation to find the spectral density functions <math>\epsilon_{a}(\theta)</math><br>
+**  equation to find the spectral density functions <math>\epsilon_{a}(\theta)</math>
-*  UV limit<br>
+*  UV limit
-**  plateau behaviour<br>
+**  plateau behaviour
-** <math>\epsilon_{a}(\theta)</math> becomes constant in a large region for <math>\theta</math> when r(inverse temperature) is small<br>
+** <math>\epsilon_{a}(\theta)</math> becomes constant in a large region for <math>\theta</math> when r(inverse temperature) is small
-*  IR limit<br>
+*  IR limit
@@ 33번째 줄: / 33번째 줄: @@
 ==limit==
-*  energy <math>E=m_{a}R\cosh \theta</math><br>
+*  energy <math>E=m_{a}R\cosh \theta</math>
-*  momentum <math>p=m_{a}R\sinh \theta</math><br>
+*  momentum <math>p=m_{a}R\sinh \theta</math>
-*  in the CFT limit, we regard \theta \to \infty for right movers and -\infty for left movers<br>
+*  in the CFT limit, we regard \theta \to \infty for right movers and -\infty for left movers
-*  Thus we get, E=p and E=-p respectively in CFT limit<br>
+*  Thus we get, E=p and E=-p respectively in CFT limit
@@ 44번째 줄: / 44번째 줄: @@
 ==TBA equation==
-*  a system which interacts dynamically via the scattering matrix and statistically via Fermi statistics:<math>Rm_{a}^{i}\cosh\theta = \epsilon_{a}^{i}(\theta)+\frac{1}{2\pi}\sum_{b=1}^{l}\sum_{j=1}^{\tilde{l}}\int_{-\infty}^{\infty} d\theta' \phi_{ab}^{ij}(\theta-\theta')\ln (1+e^{-\epsilon_{b}^{j}(\theta')})</math><br> where $R=T^{-1}$ is the inverse temperature and <math>m_{a}^{i}</math> the mass of particle (a,i)<br>
+*  a system which interacts dynamically via the scattering matrix and statistically via Fermi statistics:<math>Rm_{a}^{i}\cosh\theta = \epsilon_{a}^{i}(\theta)+\frac{1}{2\pi}\sum_{b=1}^{l}\sum_{j=1}^{\tilde{l}}\int_{-\infty}^{\infty} d\theta' \phi_{ab}^{ij}(\theta-\theta')\ln (1+e^{-\epsilon_{b}^{j}(\theta')})</math> where <math>R=T^{-1}</math> is the inverse temperature and <math>m_{a}^{i}</math> the mass of particle (a,i)
@@ 50번째 줄: / 50번째 줄: @@
 * 1 particle
 * 산란행렬
-$$
+:<math>
 S_{11}(\theta)=\tanh \left(\frac{1}{2} \left(\theta -\frac{2 i \pi }{3}\right)\right) \coth \left(\frac{1}{2} \left(\theta +\frac{2 i \pi }{3}\right)\right)
-$$
+</math>
 * 커널
-$$
+:<math>
 \phi_{11}(\theta)=-i\frac{d}{d\theta}\log S_{11}(\theta)=\sqrt{3} \left(\frac{1}{2 \cosh (\theta )+1}+\frac{1}{2 \cosh (\theta )-1}\right)
-$$
+</math>
+*
-$$
+:<math>
 N=\frac{1}{2\pi}\int_{-\infty}^{\infty}\phi_{11}(\theta)=1
-$$
+</math>

← 이전 판		2013년 3월 13일 (수) 00:11 판
74번째 줄:		74번째 줄:


		+	[[분류:통계물리]]
	[[분류:통계물리]]		[[분류:통계물리]]

← 이전 판		2013년 3월 8일 (금) 21:57 판
44번째 줄:		44번째 줄:
	==TBA equation==		==TBA equation==

−	* a system which interacts dynamically via the scattering matrix and statistically via Fermi statistics:<math>Rm_{a}^{i}\cosh\theta = \epsilon_{a}^{i}(\theta)+\sum_{b=1}^{l}\sum_{j=1}^{\tilde{l}}\int_{-\infty}^{\infty} d\theta' \phi_{ab}^{ij}(\theta-\theta')\ln (1+e^{-\epsilon_{b}^{j}(\theta')})</math><br> where $R=T^{-1}$ is the inverse temperature and <math>m_{a}^{i}</math> the mass of particle (a,i)<br>	+	* a system which interacts dynamically via the scattering matrix and statistically via Fermi statistics:<math>Rm_{a}^{i}\cosh\theta = \epsilon_{a}^{i}(\theta)+\frac{1}{2\pi}\sum_{b=1}^{l}\sum_{j=1}^{\tilde{l}}\int_{-\infty}^{\infty} d\theta' \phi_{ab}^{ij}(\theta-\theta')\ln (1+e^{-\epsilon_{b}^{j}(\theta')})</math><br> where $R=T^{-1}$ is the inverse temperature and <math>m_{a}^{i}</math> the mass of particle (a,i)<br>

← 이전 판		2013년 3월 8일 (금) 21:56 판
44번째 줄:		44번째 줄:
	==TBA equation==		==TBA equation==

−	* a system which interacts dynamically via the scattering matrix and statistically via Fermi statistics:<math>~~rm_~~{a}^{i}\cosh\theta = \epsilon_{a}^{i}(\theta)+\sum_{b=1}^{l}\sum_{j=1}^{\tilde{l}}\int_{-\infty}^{\infty} d\theta' \phi_{ab}^{ij}(\theta-\theta')\ln (1+e^{-\epsilon_{b}^{j}(\theta')})</math><br> where r is the inverse temperature and <math>m_{a}^{i}</math> the mass of particle (a,i)<br>	+	* a system which interacts dynamically via the scattering matrix and statistically via Fermi statistics:<math>Rm_{a}^{i}\cosh\theta = \epsilon_{a}^{i}(\theta)+\sum_{b=1}^{l}\sum_{j=1}^{\tilde{l}}\int_{-\infty}^{\infty} d\theta' \phi_{ab}^{ij}(\theta-\theta')\ln (1+e^{-\epsilon_{b}^{j}(\theta')})</math><br> where $R=T^{-1}$ is the inverse temperature and <math>m_{a}^{i}</math> the mass of particle (a,i)<br>

@@ 61번째 줄: / 61번째 줄: @@
 N=\frac{1}{2\pi}\int_{-\infty}^{\infty}\phi_{11}(\theta)=1
 $$
 ==관련된 항목들==

@@ 63번째 줄: / 63번째 줄: @@
 ==관련된 항목들==
-* [[대수적 베테안싸쯔]]
+* [[대수적 베테 가설 풀이(algebraic Bethe ansatz)]]
 [[분류:통계물리]]

← 이전 판		2013년 2월 25일 (월) 13:07 판
64번째 줄:		64번째 줄:
	==관련된 항목들==		==관련된 항목들==
	* [[대수적 베테안싸쯔]]		* [[대수적 베테안싸쯔]]
		+
		+
		+	[[분류:통계물리]]