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One-dimensional Bosons in Three-dimensional Traps

Elliott H. Lieb·Robert Seiringer·Jakob Yngvason
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Abstract

Recent experimental and theoretical work has indicated conditions in which a trapped, low-density Bose gas ought to behave like the 1D delta-function Bose gas solved by Lieb and Liniger. Up to now the theoretical arguments have been based on variational - perturbative ideas or numerical investigations. There are 4 parameters: density, transverse and longitudinal dimensions, and scattering length. In this paper we explicate 5 parameter regions in which various types of 1D or 3D behavior occur. Our discussion is based on a rigorous analysis of the many-body Schroedinger equation. This version of the article is a combination of the earlier 4-page arXiv version and the revised 4-page Physical Review Letters version.

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Elliott H. Lieb, Robert Seiringer, Jakob Yngvason. 2003-08-30. One-dimensional Bosons in Three-dimensional Traps. https://doi.org/10.1103/physrevlett.91.150401

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