"Simple exclusion process"의 두 판 사이의 차이
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particles jumping from left ro right or from right ro left with given probabilityes p and q (p+q=1) | particles jumping from left ro right or from right ro left with given probabilityes p and q (p+q=1) | ||
| + | |||
| + | x(t)=(x_1,\cdots,x_N) | ||
G(x,t) = probability (x(t)=x | x(0) is distributed according to g(x) ) | G(x,t) = probability (x(t)=x | x(0) is distributed according to g(x) ) | ||
| − | x | + | \frac{d}{dt}G(x,t)= L^{*}G |
| + | |||
| + | G(x,0)=\mathbf{1}(x=y) | ||
2011년 2월 9일 (수) 09:31 판
introduction
- Bethe Ansatz and Exclusion Processes [1]http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=39328&date=2011-02-01
- exclusion rule forbids to have more than one particle per site
- The simple exclusion process is a model of a lattice gas with an exclusion principle
- a particle can move to a neighboring site, with probability p to right and probability q to left, only if this is empty.
symmetric exclusion process p=q=1/2
particles jumping from left ro right or from right ro left with given probabilityes p and q (p+q=1)
x(t)=(x_1,\cdots,x_N)
G(x,t) = probability (x(t)=x | x(0) is distributed according to g(x) )
\frac{d}{dt}G(x,t)= L^{*}G
G(x,0)=\mathbf{1}(x=y)
Bethe ansatz
- Heisenberg spin chain model can be viewed as a exclusion process (time evolution)
history
encyclopedia
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://eom.springer.de
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
expositions
- 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:10.1088/0305-4470/39/41/S03.
articles
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field