"Lieb-Liniger delta Bose gas"의 두 판 사이의 차이
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* one-dimensional Bose gas<br> | * one-dimensional Bose gas<br> | ||
* 1963 Lieb and Liniger solved by [[Bethe ansatz]]<br> | * 1963 Lieb and Liniger solved by [[Bethe ansatz]]<br> | ||
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==Hamiltonian== | ==Hamiltonian== | ||
| − | * quantum mechanical Hamiltonian | + | * quantum mechanical Hamiltonian |
| − | + | :<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> | |
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* <math>s_{ab}=k_a-k_b+ic</math><br> | * <math>s_{ab}=k_a-k_b+ic</math><br> | ||
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==Bethe-ansatz equation== | ==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> | ||
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==energy spectrum== | ==energy spectrum== | ||
| − | + | * energy of a Bethe state | |
| − | <math>E=\sum_{j=1}^{N}k_j^2</math> | + | :<math>E=\sum_{j=1}^{N}k_j^2</math> |
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==related items== | ==related items== | ||
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==encyclopedia== | ==encyclopedia== | ||
| − | * http://en.wikipedia.org/wiki/ | + | * http://en.wikipedia.org/wiki/Lieb-Liniger_model |
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==articles== | ==articles== | ||
| − | + | * C. N. Yang and C. P. Yang [http://dx.doi.org/10.1063/1.1664947 Thermodynamics of a One‐Dimensional System of Bosons with Repulsive Delta‐Function Interaction], J. Math. Phys. 10, 1115 (1969) | |
| + | * C.N. Yang [http://dx.doi.org/10.1103/PhysRevLett.19.1312 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 [http://link.aps.org/doi/10.1103/PhysRev.130.1605 Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State], 1963 | ||
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[[분류:integrable systems]] | [[분류:integrable systems]] | ||
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[[분류:math and physics]] | [[분류:math and physics]] | ||
2013년 3월 4일 (월) 12:26 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
\[E=\sum_{j=1}^{N}k_j^2\]
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