Talk:Lieb-Liniger model of a Bose Gas
The Lieb-Liniger model is one among the several models that were studied by Lieb, and by Lieb and collaborators, in the sixties and solved exactly by a systematic use of the Bethe Ansatz. It provides insights, into the Bose-Einstein condensation problem, which have eventually led to the recent understanding of the Bose-Einstein phenomenon at least in several limiting situation. Here the main features of the model and of its technical solution are outlined. This is an informative, short, introduction to the subject for general audience and, at the same time, it is a stimulating guide to look and study the original work and to follow its long term implications through the selected recent references. The discussion is accurate and careful. It is therefore a model for encyclopedic articles.
The article discusses the 1D Bose gas with repulsive delta interactions, known as the Lieb-Liniger model. After an introduction, the author defines the model and describes the exact solution, based on the Bethe ansatz. He discusses how to derive in the thermodynamic limit an integral expression for the two branches of the excitations spectrum, and finally discusses recent rigorous results about the dimensional reduction of a 3D system of bosons in an alongated trap (if the trap is quasi-one dimensional, the ground state energy and the low lying excitation energies are close to the 1D ones).
The article is very well written and clear. I recommend publication on Scholarpedia.