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arXiv:0811.1166 · Journal of Statistical Physics

The Ground State Energy of the Weakly Interacting Bose Gas at High Density

Alessandro Giuliani, Robert Seiringer

Published Apr 2, 2009• 58 citations
arXivHTMLPDF
DOI
10.1007/s10955-009-9718-0

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The textbook calculation of the ground-state energy of a dilute gas of Bose particles is examined in detail, and certain mathematical inconsistencies are pointed out. On the basis of this analysis, a refined approach suitable for soft interaction potentials which lend themselves to a low-order Born approximation is developed. This procedure emphasizes the low-density character of the resulting formula for the ground-state energy, and avoids all divergent expressions at intermediate stages of the computation. It is stressed that the standard Bogoliubov approximation, if not augmented by some additional device, leads to an error which manifests itself already in the lowest order of the density. - PACS 03.75.Hh, 05.30.Jp, 03.65.Nk.
We present a novel quantum stochastic evolution equation for a matter field describing the canonical state of a weakly interacting ultracold Bose gas. In the ideal gas limit our approach is exact. This numerically very stable equation suppresses high-energy fluctuations exponentially, which enables us to describe condensed and thermal atoms within the same formalism. We present applications to ground-state occupation and fluctuations, density profile of ground-state and thermal cloud, and ground-state number statistics. Our main aim are spatial coherence properties which we investigate through the determination of interference contrast and spatial density correlations. Parameters are taken from actual experiments.