Lieb-Liniger delta Bose gas

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

• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

 

 

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

• 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)

• http://mathoverflow.net/search?q=
• http://mathoverflow.net/search?q=

 

 

blogs

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=
  • http://blogsearch.google.com/blogsearch?q=

 

 

experts on the field

• http://arxiv.org/

 

 

links

• Detexify2 - LaTeX symbol classifier
• 수식표현 안내
• The On-Line Encyclopedia of Integer Sequences
• http://functions.wolfram.com/