"Universal chiral partition function"의 두 판 사이의 차이
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==introduction== | ==introduction== | ||
| − | * grand partition function for n species of right moving (chiral) particles with fugacities z | + | * grand partition function for n species of right moving (chiral) particles with fugacities z |
* N개의 보존 입자가 있고, 에너지의 단위를 <math>\hbar\omega=1</math>으로 하여, 에너지레벨이 <math>E_0,E_1,E_2,\cdots</math> 인 시스템을 생각하자. | * N개의 보존 입자가 있고, 에너지의 단위를 <math>\hbar\omega=1</math>으로 하여, 에너지레벨이 <math>E_0,E_1,E_2,\cdots</math> 인 시스템을 생각하자. | ||
| 38번째 줄: | 38번째 줄: | ||
==special cases== | ==special cases== | ||
| − | * rank 1 case examples | + | * rank 1 case examples |
| − | * Berkovich1998 and Wu's paper | + | * Berkovich1998 and Wu's paper |
| 55번째 줄: | 55번째 줄: | ||
==related items== | ==related items== | ||
| − | * [[fractional and exclusion statistics]] | + | * [[fractional and exclusion statistics]] |
| − | * [[Fermionic summation formula]] | + | * [[Fermionic summation formula]] |
| 76번째 줄: | 76번째 줄: | ||
| − | * [[2010년 books and articles]] | + | * [[2010년 books and articles]] |
* http://gigapedia.info/1/ | * http://gigapedia.info/1/ | ||
* http://gigapedia.info/1/ | * http://gigapedia.info/1/ | ||
| 89번째 줄: | 89번째 줄: | ||
==articles== | ==articles== | ||
| − | * [http://arxiv.org/abs/hep-th/9903176 Exclusion statistics in conformal field theory and the UCPF for WZW models] | + | * [http://arxiv.org/abs/hep-th/9903176 Exclusion statistics in conformal field theory and the UCPF for WZW models] |
** Peter Bouwknegt, Leung Chim, David Ridout, 1999 | ** Peter Bouwknegt, Leung Chim, David Ridout, 1999 | ||
| − | * [http://arxiv.org/abs/hep-th/9808171 Comment on the paper ``The universal chiral partition function for exclusion statistics''] | + | * [http://arxiv.org/abs/hep-th/9808171 Comment on the paper ``The universal chiral partition function for exclusion statistics''] |
| − | ** K. Schoutens (University of Amsterdam) | + | ** K. Schoutens (University of Amsterdam) |
* Berkovich, A., 와/과B. M McCoy. 1998. “The universal chiral partition function for exclusion statistics”. <em>hep-th/9808013</em> (8월 4). http://arxiv.org/abs/hep-th/9808013 | * Berkovich, A., 와/과B. M McCoy. 1998. “The universal chiral partition function for exclusion statistics”. <em>hep-th/9808013</em> (8월 4). http://arxiv.org/abs/hep-th/9808013 | ||
| − | * [http://dx.doi.org/10.1103/PhysRevLett.73.922 Statistical distribution for generalized ideal gas of fractional-statistics particles] | + | * [http://dx.doi.org/10.1103/PhysRevLett.73.922 Statistical distribution for generalized ideal gas of fractional-statistics particles] |
** Y.S. Wu,, Phys. Rev. Letts. 73 (1994) 922 | ** Y.S. Wu,, Phys. Rev. Letts. 73 (1994) 922 | ||
| 101번째 줄: | 101번째 줄: | ||
* http://www.zentralblatt-math.org/zmath/en/ | * http://www.zentralblatt-math.org/zmath/en/ | ||
* http://pythagoras0.springnote.com/ | * http://pythagoras0.springnote.com/ | ||
| − | + | [http://www.ams.org/mathscinet ] | |
* http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q= | * http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q= | ||
* http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7= | * http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7= | ||
| 121번째 줄: | 121번째 줄: | ||
==blogs== | ==blogs== | ||
| − | * 구글 블로그 검색 | + | * 구글 블로그 검색 |
** http://blogsearch.google.com/blogsearch?q= | ** http://blogsearch.google.com/blogsearch?q= | ||
** http://blogsearch.google.com/blogsearch?q= | ** http://blogsearch.google.com/blogsearch?q= | ||
2020년 11월 14일 (토) 02:26 판
introduction
- grand partition function for n species of right moving (chiral) particles with fugacities z
- N개의 보존 입자가 있고, 에너지의 단위를 \(\hbar\omega=1\)으로 하여, 에너지레벨이 \(E_0,E_1,E_2,\cdots\) 인 시스템을 생각하자.
N개의 입자가 있는 보존 시스템의 분배함수를 \(Z_B(N)\) 이라 두자.
큰 분배함수(grand partition function)는 \(Z_G=\sum_{n=0}^{\infty}Z_B(N)z^N\) 으로 쓸수 있다.
\(n_0,n_1,n_2,\cdots\) 은 각각 에너지가 \(E_0,E_1,E_2,\cdots\)인 입자의 수라고 하자.
\(Z_B(N)=\sum_{\sum n_r=N}\exp(-\beta\sum_{r}n_r E_r)\) 이므로,
\(Z_G=\sum_{N=0}^{\infty}Z_B(N)z^N=\sum_{N=0}^{\infty} \sum_{\sum n_r=N}\exp(-\beta\sum_{r}n_r E_r)z^N\)
\(=\prod_{r=0}^{\infty}\sum_{n_r=0}^{\infty} (ze^{-\beta E_r})^{n_r}=\prod_{r=0}\frac{1}{1-ze^{-\beta E_r}}\)
physical meaning
\(f_{A,B,C}(\tau)=\sum_{n\in \mathbb{Z}_{\geq 0}^r}\frac {q^{\frac{1}{2}n^{t}An+B^{t}\cdot n+C}} {(q)_{n_1}\cdots(q)_{n_r}}\)
A: energy shift due to interaction
B : energy shift due to (global) statistics
C : ground state Casimir energy
special cases
- rank 1 case examples
- Berkovich1998 and Wu's paper
history
encyclopedia
books
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
articles
- Exclusion statistics in conformal field theory and the UCPF for WZW models
- Peter Bouwknegt, Leung Chim, David Ridout, 1999
- Comment on the paper ``The universal chiral partition function for exclusion statistics
- K. Schoutens (University of Amsterdam)
- Berkovich, A., 와/과B. M McCoy. 1998. “The universal chiral partition function for exclusion statistics”. hep-th/9808013 (8월 4). http://arxiv.org/abs/hep-th/9808013
- Statistical distribution for generalized ideal gas of fractional-statistics particles
- Y.S. Wu,, Phys. Rev. Letts. 73 (1994) 922
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- http://dx.doi.org/
question and answers(Math Overflow)
blogs
experts on the field