"Hubbard model"의 두 판 사이의 차이
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2012년 10월 29일 (월) 09:55 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
- 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