The Lieb-Liniger model as a limit of dilute bosons in three dimensions Journal Article


Author(s): Seiringer, Robert; Yin, Jun
Article Title: The Lieb-Liniger model as a limit of dilute bosons in three dimensions
Affiliation
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.
Journal Title: Communications in Mathematical Physics
Volume: 284
Issue 2
ISSN: 1432-0916
Publisher: Springer  
Date Published: 2008-12-01
Start Page: 459
End Page: 479
URL:
DOI: 10.1007/s00220-008-0521-6
Open access: yes (repository)
IST Austria Authors
  1. Robert Seiringer
    123 Seiringer
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