"Lieb-Liniger delta Bose gas"의 두 판 사이의 차이
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| 1번째 줄: | 1번째 줄: | ||
| − | + | ==introduction== | |
* N bosons interacting on a line of length L via the delta function potential<br> | * N bosons interacting on a line of length L via the delta function potential<br> | ||
| 11번째 줄: | 11번째 줄: | ||
| − | + | ==Hamiltonian== | |
* quantum mechanical Hamiltonian<br><math>H=-\sum_{j=1}^{N}\frac{\partial^2}{\partial x_j^2}+2c\sum_{1\leq i<j\leq N}^{N}\delta(x_i-x_j)</math><br> | * quantum mechanical Hamiltonian<br><math>H=-\sum_{j=1}^{N}\frac{\partial^2}{\partial x_j^2}+2c\sum_{1\leq i<j\leq N}^{N}\delta(x_i-x_j)</math><br> | ||
| 21번째 줄: | 21번째 줄: | ||
| − | + | ==two-body scattering term== | |
* <math>s_{ab}=k_a-k_b+ic</math><br> | * <math>s_{ab}=k_a-k_b+ic</math><br> | ||
| 29번째 줄: | 29번째 줄: | ||
| − | + | ==Bethe-ansatz equation== | |
<math>\exp(ik_jL)=\prod_{l=1}^{N}\frac{k_j-k_l+ic}{k_j-k_l-ic}</math> | <math>\exp(ik_jL)=\prod_{l=1}^{N}\frac{k_j-k_l+ic}{k_j-k_l-ic}</math> | ||
| 37번째 줄: | 37번째 줄: | ||
| − | + | ==energy spectrum== | |
<math>E=\sum_{j=1}^{N}k_j^2</math> | <math>E=\sum_{j=1}^{N}k_j^2</math> | ||
| 47번째 줄: | 47번째 줄: | ||
| − | + | ==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== | |
| 61번째 줄: | 61번째 줄: | ||
| − | + | ==encyclopedia== | |
* http://en.wikipedia.org/wiki/ | * http://en.wikipedia.org/wiki/ | ||
| 71번째 줄: | 71번째 줄: | ||
| − | + | ==books== | |
| 86번째 줄: | 86번째 줄: | ||
| − | + | ==articles== | |
| 108번째 줄: | 108번째 줄: | ||
| − | + | ==question and answers(Math Overflow)== | |
* http://mathoverflow.net/search?q= | * http://mathoverflow.net/search?q= | ||
| 117번째 줄: | 117번째 줄: | ||
| − | + | ==blogs== | |
* 구글 블로그 검색<br> | * 구글 블로그 검색<br> | ||
| 127번째 줄: | 127번째 줄: | ||
| − | + | ==experts on the field== | |
* http://arxiv.org/ | * http://arxiv.org/ | ||
| 135번째 줄: | 135번째 줄: | ||
| − | + | ==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) 17:38 판
introduction
- N bosons interacting on a line of length L via the delta function potential
- one-dimensional Bose gas
- 1963 Lieb and Liniger solved by Bethe ansatz
Hamiltonian
- quantum mechanical Hamiltonian
\(H=-\sum_{j=1}^{N}\frac{\partial^2}{\partial x_j^2}+2c\sum_{1\leq i<j\leq N}^{N}\delta(x_i-x_j)\)
two-body scattering term
- \(s_{ab}=k_a-k_b+ic\)
Bethe-ansatz equation
\(\exp(ik_jL)=\prod_{l=1}^{N}\frac{k_j-k_l+ic}{k_j-k_l-ic}\)
energy spectrum
\(E=\sum_{j=1}^{N}k_j^2\)
history
encyclopedia
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
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
- Thermodynamics of a One‐Dimensional System of Bosons with Repulsive Delta‐Function Interaction
- C. N. Yang and C. P. Yang, J. Math. Phys. 10, 1115 (1969)
- Some exact results for the many-body problem in one dimension with repulsive delta-function interaction
- C.N. Yang, Phys. Rev. Lett. 19 (1967), 1312-1315
- Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State
- Elliott H. Lieb and Werner Liniger, 1963
- http://www.ams.org/mathscinet
- [1]http://www.zentralblatt-math.org/zmath/en/
- [2]http://arxiv.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
blogs
experts on the field