Lieb-Liniger delta Bose gas

수학노트
http://bomber0.myid.net/ (토론)님의 2012년 8월 26일 (일) 13:19 판
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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

 

 

related items

 

 

encyclopedia

 

 

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[[4909919|]]

 

 

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question and answers(Math Overflow)

 

 

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