Author(s):

Seiringer, Robert; Yin, Jun

Article Title: 
The LiebLiniger model as a limit of dilute bosons in three dimensions

Affiliation 

Abstract: 
We show that the LiebLiniger model for onedimensional bosons with repulsive δfunction interaction can be rigorously derived via a scaling limit from a dilute threedimensional 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 threedimensional bosons in strongly elongated traps and relate them to the corresponding quantities in the LiebLiniger model. In particular, if both the scattering length a and the radius r of the cylindrical trap go to zero, the LiebLiniger 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 threedimensional bosons in a spectral window of size ∼ r 2 above the ground state energy.

Journal Title:

Communications in Mathematical Physics

Volume: 
284

Issue 
2

ISSN:

14320916

Publisher:

Springer

Date Published:

20081201

Start Page: 
459

End Page:

479

URL: 

DOI: 
10.1007/s0022000805216

Open access: 
yes (repository) 