Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic Gases

Details Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic Gases Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic Gases

2002-10-29

arxiv.org/abs/cond-mat/0210629v3

Physics

Condensed Matter

A significant misprint in the definition of c_2 is corrected. 5 pages, 1 EPS figure, references updated

Scientific paper

10.1103/PhysRevLett.91.090401

We derive exact closed form expressions for the first few terms of the short-distance Taylor expansion of the one-body correlation function of the Lieb-Liniger gas. As an intermediate result we obtain the high-p asymptotics of the momentum distribution of both free and harmonically trapped atoms and show that it obeys a universal 1/p^4 law for_all_ values of the interaction strength. We discuss the ways to observe the predicted momentum distributions experimentally, regarding them as a sensitive identifier for the Tonks-Girardeau regime of strong correlations.

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