Simple exclusion process - 편집 역사

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 [[분류:migrate]]
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q297612 Q297612]

← 이전 판		2020년 12월 28일 (월) 12:44 판
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	[[분류:math and physics]]		[[분류:math and physics]]
	[[분류:migrate]]		[[분류:migrate]]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q297612 Q297612]

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-−
 ==related items==
@@ 74번째 줄: / 74번째 줄: @@
 * Mallick, Kirone. ‘The Exclusion Process: A Paradigm for Non-Equilibrium Behaviour’. arXiv:1412.6258 [cond-Mat], 19 December 2014. http://arxiv.org/abs/1412.6258.
 * Kaufmann, [https://docs.google.com/file/d/0B8XXo8Tve1cxemM0a05MbDFuYkU/edit Bethe ansatz for two species totally asymmetric diffusion]
 * Golinelli, Olivier, and Kirone Mallick. 2006. The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics. Journal of Physics A: Mathematical and General 39, no. 41 (10): 12679-12705. doi:[http://dx.doi.org/10.1088/0305-4470/39/41/S03 10.1088/0305-4470/39/41/S03].
-−
 ==articles==
@@ 98번째 줄: / 98번째 줄: @@
 * Derrida, B. “An Exactly Soluble Non-Equilibrium System: The Asymmetric Simple Exclusion Process.” Physics Reports 301, no. 1–3 (July 1, 1998): 65–83. doi:10.1016/S0370-1573(98)00006-4.
 * Schütz, Gunter M. 1997. Exact solution of the master equation for the asymmetric exclusion process. Journal of Statistical Physics 88, no. 1 (7): 427-445. doi:[http://dx.doi.org/10.1007/BF02508478 10.1007/BF02508478].
 * Gwa, Leh-Hun, and Herbert Spohn. 1992. “Bethe Solution for the Dynamical-scaling Exponent of the Noisy Burgers Equation.” Physical Review A 46 (2) (July 15): 844–854. doi:http://dx.doi.org/10.1103/PhysRevA.46.844.
 ===random growth model===

@@ 12번째 줄: / 12번째 줄: @@
 * a particle can move to a neighboring site, with probability p to right and probability q to left, only if this is empty.
 *  special cases
-** symmetric exclusion process $p=q=1/2$
+** symmetric exclusion process <math>p=q=1/2</math>
-** asymmetric simple exclusion process (ASEP) $p\neq q$
+** asymmetric simple exclusion process (ASEP) <math>p\neq q</math>
-** totally asymmetric exclusion process (TASEP) $p=1,q=0$
+** totally asymmetric exclusion process (TASEP) <math>p=1,q=0</math>
-* for example, $\delta=\gamma=q=0$ model for traffic flow
+* for example, <math>\delta=\gamma=q=0</math> model for traffic flow
-* particles jumping from left ro right or from right ro left with given probabilities $p$ and $q$ ($p+q=1$)
+* particles jumping from left ro right or from right ro left with given probabilities <math>p</math> and <math>q</math> (<math>p+q=1</math>)
 ===dynamical rules===
-* $P(C,t)$ be the probability for configuration $C$ at time $t$
+* <math>P(C,t)</math> be the probability for configuration <math>C</math> at time <math>t</math>
-* $P(C,t)$ is a solution of the master equation
+* <math>P(C,t)</math> is a solution of the master equation
-$$
+:<math>
 \frac{\partial P(C,t)}{\partial t}=\sum_{C':C'\neq C}P(C',t)W(C'\to C)-\left(\sum_{C':C'\neq C}W(C\to C')\right)P(C,t)
-$$
+</math>
 * [[Master equation for asymmetric simple exclusion process]]
@@ 32번째 줄: / 32번째 줄: @@
 ===critical exponent===
-* relaxation time $\tau$ towards equilibrium
+* relaxation time <math>\tau</math> towards equilibrium
-* spatial correlation length $\xi$
+* spatial correlation length <math>\xi</math>
-* dynamical critical exponent $z$ given by $\tau \sim \xi^z$
+* dynamical critical exponent <math>z</math> given by <math>\tau \sim \xi^z</math>
-* for one-dimensional quantum spin chains $\tau \sim L^z$ where $L$ is the length of the spin chain
+* for one-dimensional quantum spin chains <math>\tau \sim L^z</math> where <math>L</math> is the length of the spin chain
 ===Bethe ansatz===
-$\tau$ is dominated by the eigenvalue of the Hamiltonian with the smallest real part
+<math>\tau</math> is dominated by the eigenvalue of the Hamiltonian with the smallest real part
 * thus the finite size analysis of the Hamiltonian gives
-$$
+:<math>
 \Re(E_1)\sim \frac{1}{L^z}
-$$
+</math>
-* so we need to compute $E_1$ to get $z$
+* so we need to compute <math>E_1</math> to get <math>z</math>
 * this is where the [[Bethe ansatz]] comes in
@@ 83번째 줄: / 83번째 줄: @@
 * Cantini, Luigi, Jan de Gier, and Michael Wheeler. “Matrix Product and Sum Rule for Macdonald Polynomials.” arXiv:1602.04392 [math-Ph], February 13, 2016. http://arxiv.org/abs/1602.04392.
 * Sato, Jun, and Katsuhiro Nishinari. “Exact Relaxation Dynamics of the ASEP with Langmuir Kinetics on a Ring.” arXiv:1601.02651 [cond-Mat, Physics:math-Ph, Physics:nlin], January 7, 2016. http://arxiv.org/abs/1601.02651.
-* Kuniba, Atsuo, Shouya Maruyama, and Masato Okado. “Multispecies Totally Asymmetric Zero Range Process: I. Multiline Process and Combinatorial $R$.” arXiv:1511.09168 [cond-Mat, Physics:math-Ph, Physics:nlin], November 30, 2015. http://arxiv.org/abs/1511.09168.
+* Kuniba, Atsuo, Shouya Maruyama, and Masato Okado. “Multispecies Totally Asymmetric Zero Range Process: I. Multiline Process and Combinatorial <math>R</math>.” arXiv:1511.09168 [cond-Mat, Physics:math-Ph, Physics:nlin], November 30, 2015. http://arxiv.org/abs/1511.09168.
 * Crampe, N., L. Frappat, E. Ragoucy, and M. Vanicat. “A New Braid-like Algebra for Baxterisation.” arXiv:1509.05516 [math-Ph], September 18, 2015. http://arxiv.org/abs/1509.05516.
-* Kuniba, Atsuo, Shouya Maruyama, and Masato Okado. “Multispecies TASEP and Combinatorial $R$.” arXiv:1506.04490 [math-Ph, Physics:nlin], June 15, 2015. http://arxiv.org/abs/1506.04490.
+* Kuniba, Atsuo, Shouya Maruyama, and Masato Okado. “Multispecies TASEP and Combinatorial <math>R</math>.” arXiv:1506.04490 [math-Ph, Physics:nlin], June 15, 2015. http://arxiv.org/abs/1506.04490.
 * Ortmann, Janosch, Jeremy Quastel, and Daniel Remenik. “A Pfaffian Representation for Flat ASEP.” arXiv:1501.05626 [math-Ph], January 22, 2015. http://arxiv.org/abs/1501.05626.
-* Barraquand, Guillaume, and Ivan Corwin. “The $q$-Hahn Asymmetric Exclusion Process.” arXiv:1501.03445 [cond-Mat, Physics:math-Ph], January 14, 2015. http://arxiv.org/abs/1501.03445.
+* Barraquand, Guillaume, and Ivan Corwin. “The <math>q</math>-Hahn Asymmetric Exclusion Process.” arXiv:1501.03445 [cond-Mat, Physics:math-Ph], January 14, 2015. http://arxiv.org/abs/1501.03445.
 * Crampe, Nicolas. “Algebraic Bethe Ansatz for the Totally Asymmetric Simple Exclusion Process with Boundaries.” arXiv:1411.7954 [cond-Mat, Physics:math-Ph, Physics:nlin], November 28, 2014. http://arxiv.org/abs/1411.7954.
 * Prolhac, Sylvain. “Asymptotics for the Norm of Bethe Eigenstates in the Periodic Totally Asymmetric Exclusion Process.” arXiv:1411.7008 [cond-Mat, Physics:math-Ph, Physics:nlin], November 25, 2014. http://arxiv.org/abs/1411.7008.

← 이전 판		2020년 11월 13일 (금) 13:32 판
107번째 줄:		107번째 줄:
	[[분류:integrable systems]]		[[분류:integrable systems]]
	[[분류:math and physics]]		[[분류:math and physics]]
		+	[[분류:migrate]]

← 이전 판		2016년 5월 6일 (금) 04:05 판
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		+	==articles 2==
	===single species model===		===single species model===
	* Tracy, Craig A., and Harold Widom. 2009. Asymptotics in ASEP with Step Initial Condition. Communications in Mathematical Physics 290, no. 1 (2): 129-154. doi:[http://dx.doi.org/10.1007/s00220-009-0761-0 10.1007/s00220-009-0761-0].		* Tracy, Craig A., and Harold Widom. 2009. Asymptotics in ASEP with Step Initial Condition. Communications in Mathematical Physics 290, no. 1 (2): 129-154. doi:[http://dx.doi.org/10.1007/s00220-009-0761-0 10.1007/s00220-009-0761-0].

@@ 79번째 줄: / 79번째 줄: @@
 ==articles==
-* Sylvain Prolhac, Finite-time fluctuations for the totally asymmetric exclusion process, 10.1103/PhysRevLett.116.090601, http://dx.doi.org/10.1103/PhysRevLett.116.090601, Phys. Rev. Lett. 116 (2016) 090601, http://arxiv.org/abs/1511.04064v3
+* Cantini, Luigi, Jan de Gier, and Michael Wheeler. “Matrix Product and Sum Rule for Macdonald Polynomials.” arXiv:1602.04392 [math-Ph], February 13, 2016. http://arxiv.org/abs/1602.04392.
 * Johansson, Kurt. 2000. Shape Fluctuations and Random Matrices. Communications in Mathematical Physics 209, no. 2 (2): 437-476. doi:[http://dx.doi.org/10.1007/s002200050027 10.1007/s002200050027].