"Lieb-Liniger delta Bose gas"의 두 판 사이의 차이
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==computational resource== | ==computational resource== | ||
| − | * Day 5 - Yang-Baxter, Delta Bosons, Contact Terms | + | * [http://msstp.org/?q=node/275 Day 5 - Yang-Baxter, Delta Bosons, Contact Terms] |
** [http://msstp.org/sites/default/files/Problems4.pdf Bose-Einstein Condensation and BAE exercise .pdf] | ** [http://msstp.org/sites/default/files/Problems4.pdf Bose-Einstein Condensation and BAE exercise .pdf] | ||
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** [http://msstp.org/sites/default/files/problem4.nb Bose-Einstein Condensation and BAE solution .nb] | ** [http://msstp.org/sites/default/files/problem4.nb Bose-Einstein Condensation and BAE solution .nb] | ||
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==encyclopedia== | ==encyclopedia== | ||
2013년 3월 4일 (월) 13:02 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
- energy of a Bethe state
\[E=\sum_{j=1}^{N}k_j^2\]
computational resource
encyclopedia
articles
- C. N. Yang and C. P. Yang Thermodynamics of a One‐Dimensional System of Bosons with Repulsive Delta‐Function Interaction, J. Math. Phys. 10, 1115 (1969)
- C.N. Yang Some exact results for the many-body problem in one dimension with repulsive delta-function interaction, Phys. Rev. Lett. 19 (1967), 1312-1315
- Elliott H. Lieb and Werner Liniger Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State, 1963