{"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0709.4022"}],"volume":284,"intvolume":"       284","extern":1,"publication_status":"published","publist_id":"4544","citation":{"ama":"Seiringer R, Yin J. The Lieb-Liniger model as a limit of dilute bosons in three dimensions. <i>Communications in Mathematical Physics</i>. 2008;284(2):459-479. doi:<a href=\"https://doi.org/10.1007/s00220-008-0521-6\">10.1007/s00220-008-0521-6</a>","short":"R. Seiringer, J. Yin, Communications in Mathematical Physics 284 (2008) 459–479.","mla":"Seiringer, Robert, and Jun Yin. “The Lieb-Liniger Model as a Limit of Dilute Bosons in Three Dimensions.” <i>Communications in Mathematical Physics</i>, vol. 284, no. 2, Springer, 2008, pp. 459–79, doi:<a href=\"https://doi.org/10.1007/s00220-008-0521-6\">10.1007/s00220-008-0521-6</a>.","ieee":"R. Seiringer and J. Yin, “The Lieb-Liniger model as a limit of dilute bosons in three dimensions,” <i>Communications in Mathematical Physics</i>, vol. 284, no. 2. Springer, pp. 459–479, 2008.","ista":"Seiringer R, Yin J. 2008. The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in Mathematical Physics. 284(2), 459–479.","apa":"Seiringer, R., &#38; Yin, J. (2008). The Lieb-Liniger model as a limit of dilute bosons in three dimensions. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-008-0521-6\">https://doi.org/10.1007/s00220-008-0521-6</a>","chicago":"Seiringer, Robert, and Jun Yin. “The Lieb-Liniger Model as a Limit of Dilute Bosons in Three Dimensions.” <i>Communications in Mathematical Physics</i>. Springer, 2008. <a href=\"https://doi.org/10.1007/s00220-008-0521-6\">https://doi.org/10.1007/s00220-008-0521-6</a>."},"page":"459 - 479","publisher":"Springer","day":"01","date_created":"2018-12-11T11:57:21Z","author":[{"last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer"},{"last_name":"Yin","first_name":"Jun","full_name":"Yin, Jun"}],"doi":"10.1007/s00220-008-0521-6","date_updated":"2021-01-12T06:57:08Z","publication":"Communications in Mathematical Physics","type":"journal_article","quality_controlled":0,"oa":1,"status":"public","issue":"2","_id":"2382","title":"The Lieb-Liniger model as a limit of dilute bosons in three dimensions","abstract":[{"text":"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.","lang":"eng"}],"year":"2008","date_published":"2008-12-01T00:00:00Z","month":"12"}