"Hubbard model"의 두 판 사이의 차이
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encyclopedia==
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| 1번째 줄: | 1번째 줄: | ||
| − | ==introduction | + | ==introduction== |
* The Hubbard model describes hopping electrons on a lattice | * The Hubbard model describes hopping electrons on a lattice | ||
| 14번째 줄: | 14번째 줄: | ||
| − | ==Lieb-Wu equations | + | ==Lieb-Wu equations== |
* describing Eigenstates of the Hubbard Hamiltonian<br><math>\exp(ik_jL)=\prod_{l=1}^{M}\frac{\lambda_{l}-\sin k_j-i u}{\lambda_{l}-\sin k_j+i u}</math>, <math>j=1,\cdots, N</math><br><math>\prod_{j=1}^{N}\frac{\lambda_{l}-\sin k_j-i u}{\lambda_{l}-\sin k_j+i u}=\prod_{m=1,m\neq l}^{M}\frac{\lambda_{l}-\lambda_{m}-2i u}{\lambda_{l}-\lambda_{m}+2i u}</math>, <math>l=1,\cdots, M</math><br> | * describing Eigenstates of the Hubbard Hamiltonian<br><math>\exp(ik_jL)=\prod_{l=1}^{M}\frac{\lambda_{l}-\sin k_j-i u}{\lambda_{l}-\sin k_j+i u}</math>, <math>j=1,\cdots, N</math><br><math>\prod_{j=1}^{N}\frac{\lambda_{l}-\sin k_j-i u}{\lambda_{l}-\sin k_j+i u}=\prod_{m=1,m\neq l}^{M}\frac{\lambda_{l}-\lambda_{m}-2i u}{\lambda_{l}-\lambda_{m}+2i u}</math>, <math>l=1,\cdots, M</math><br> | ||
| 24번째 줄: | 24번째 줄: | ||
| − | ==string hypothesis | + | ==string hypothesis== |
| 32번째 줄: | 32번째 줄: | ||
| − | ==history | + | ==history== |
* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
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| − | ==related items | + | ==related items== |
* | * | ||
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| − | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103);">encyclopedia | + | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103);">encyclopedia== |
* http://en.wikipedia.org/wiki/Hubbard_model | * http://en.wikipedia.org/wiki/Hubbard_model | ||
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| − | ==books | + | ==books== |
* [http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521802628 The One-Dimensional Hubbard Model] | * [http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521802628 The One-Dimensional Hubbard Model] | ||
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| − | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103);">articles | + | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103);">articles== |
* [http://dx.doi.org/10.1143/JPSJ.56.1340 Lax Pair for the One-Dimensional Hubbard Model]<br> | * [http://dx.doi.org/10.1143/JPSJ.56.1340 Lax Pair for the One-Dimensional Hubbard Model]<br> | ||
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| − | ==question and answers(Math Overflow) | + | ==question and answers(Math Overflow)== |
* http://mathoverflow.net/search?q= | * http://mathoverflow.net/search?q= | ||
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| − | ==blogs | + | ==blogs== |
* 구글 블로그 검색<br> | * 구글 블로그 검색<br> | ||
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| − | ==experts on the field | + | ==experts on the field== |
* http://arxiv.org/ | * http://arxiv.org/ | ||
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| − | ==links | + | ==links== |
* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | * [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | ||
2012년 10월 28일 (일) 14:29 판
introduction
- The Hubbard model describes hopping electrons on a lattice
- 1968 Lieb and We
- application of Bethe ansatz
- 1972 Takahasi
- string hypothesis
- replace the Lieb-Wu equations by simpler ones
- proceeded to drive a set of non-linear integral equations known as thermodynamic Bethe ansatz equations
- algebraic Bethe ansatz for the Hubbard model
Lieb-Wu equations
- describing Eigenstates of the Hubbard Hamiltonian
\(\exp(ik_jL)=\prod_{l=1}^{M}\frac{\lambda_{l}-\sin k_j-i u}{\lambda_{l}-\sin k_j+i u}\), \(j=1,\cdots, N\)
\(\prod_{j=1}^{N}\frac{\lambda_{l}-\sin k_j-i u}{\lambda_{l}-\sin k_j+i u}=\prod_{m=1,m\neq l}^{M}\frac{\lambda_{l}-\lambda_{m}-2i u}{\lambda_{l}-\lambda_{m}+2i u}\), \(l=1,\cdots, M\)
string hypothesis
history
encyclopedia==
- http://en.wikipedia.org/wiki/Hubbard_model
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- The One-Dimensional Hubbard Model
- 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==
- Lax Pair for the One-Dimensional Hubbard Model
- Miki Wadati, Eugenio Olmedilla and Yasuhiro Akutsu, 1986
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/10.1143/JPSJ.56.1340
question and answers(Math Overflow)
blogs
experts on the field
links
- Lax Pair for the One-Dimensional Hubbard Model
- Miki Wadati, Eugenio Olmedilla and Yasuhiro Akutsu, 1986
- Miki Wadati, Eugenio Olmedilla and Yasuhiro Akutsu, 1986
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/10.1143/JPSJ.56.1340
question and answers(Math Overflow)
blogs
experts on the field