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調和トラップ中の1次元ボース系の理論(4)

正人 大矢

Published Mar 24, 2009• 0 citations
OpenAlex

Abstract

We consider a one-dimensional two-level system of repulsive δ-interacting bosons trapped in a har­monic potential. For all values of the coupling strength, we derive expressions of the wave functions of three, four, five, six-body systems.

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A one-dimensional system consisting of equal numbers of two types of bosons undergoing interactions through delta function potentials is examined. All particles have the same mass but each boson carries a "charge" that distinguishes one boson type from the other. The interactions are such that like particles repel and unlike attract. The amount of attraction and/or repulsion is determined by two adjustable parameters so that the amount of repulsion is not necessary equal to that of attraction.
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Motivated by recent experiments we derive an exact expression for the correlation function entering the three-body recombination rate for a one-dimensional gas of interacting bosons. The answer, given in terms of two thermodynamic parameters of the Lieb-Liniger model, is valid for all values of the dimensionless coupling $\ensuremath{\gamma}$ and contains the previously known results for the Bogoliubov and Tonks-Girardeau regimes as limiting cases. We also investigate finite-size effects by calculating the correlation function for small systems of three, four, five, and six particles.