@article{2382, abstract = {We show that the Lieb-Liniger model for one-dimensional bosons with repulsive δ-function interaction can be rigorously derived via a scaling limit from a dilute three-dimensional Bose gas with arbitrary repulsive interaction potential of finite scattering length. For this purpose, we prove bounds on both the eigenvalues and corresponding eigenfunctions of three-dimensional bosons in strongly elongated traps and relate them to the corresponding quantities in the Lieb-Liniger model. In particular, if both the scattering length a and the radius r of the cylindrical trap go to zero, the Lieb-Liniger model with coupling constant g ∼ a/r 2 is derived. Our bounds are uniform in g in the whole parameter range 0 ≤ g ≤ ∞, and apply to the Hamiltonian for three-dimensional bosons in a spectral window of size ∼ r -2 above the ground state energy.}, author = {Robert Seiringer and Yin, Jun}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {459 -- 479}, publisher = {Springer}, title = {{The Lieb-Liniger model as a limit of dilute bosons in three dimensions}}, doi = {10.1007/s00220-008-0521-6}, volume = {284}, year = {2008}, }