We report on a rigorous analysis of the ground state of a dilute Bose gas in an external confining potential in the limit where the confinement becomes very strong in two dimensions and as a result the system behaves essentially one-dimensional. We show that the system is well described by a one-dimensional model of Bosons with delta function interaction that was solved long ago by Lieb and Liniger. We explicate 5 parameter regions in which various types of behavior of the system occur. This is relevant for the interpretation of recent experiments on ultra-cold atomic gases in strongly elongated traps.
|Title of host publication
|XIVth International Congress on Mathematical Physics
|Subtitle of host publication
|Lisbon, 28 July - 2 August 2003
|World Scientific Publishing Co.
|Number of pages
|Published - Jan 1 2006
All Science Journal Classification (ASJC) codes
- General Physics and Astronomy