# Mathematics Colloquia and Seminars

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### One-dimensional behavior of dilute, trapped Bose gases

**Mathematical Physics & Probability**

Speaker: | Robert Seiringer, Princeton |

Location: | 693 Kerr |

Start time: | Fri, Jan 23 2004, 4:10PM |

Recent experimental and theoretical work has shown that there are conditions in which trapped, low-density Bose gases behave like one-dimensional systems. These are typically described by a model of a 1D Bose gas with delta-function interaction, solved exactly by Lieb and Liniger long ago. This one-dimensional behavior is an intrinsically quantum-mechanical phenomenon. We give a rigorous proof of it, as far as the ground state energy and particle density is concerned, and determine the relevant parameter regimes. In particular, we derive the 1D Bose gas with delta-function interaction as a limit of a 3D Bose gas of hard spheres.