Lieb-Liniger delta Bose gas
imported>Pythagoras0님의 2012년 10월 28일 (일) 15:31 판 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로)
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
\(H=-\sum_{j=1}^{N}\frac{\partial^2}{\partial x_j^2}+2c\sum_{1\leq i<j\leq N}^{N}\delta(x_i-x_j)\)
\(H=-\sum_{j=1}^{N}\frac{\partial^2}{\partial x_j^2}+2c\sum_{1\leq i<j\leq N}^{N}\delta(x_i-x_j)\)
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==
related items==
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=
4909919
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
- C. N. Yang and C. P. Yang, J. Math. Phys. 10, 1115 (1969)
- C.N. Yang, Phys. Rev. Lett. 19 (1967), 1312-1315
- Elliott H. Lieb and Werner Liniger, 1963