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Journal of Mathematical Physics

Cluster coefficients for the one-dimensional Bose gas with point interactions

L. R. Dodd, Anne-Marie Gibbs

Published Jan 1, 1974• 6 citations
Publisher

Abstract

Exact expressions for the cluster coefficients b2 and b3 for the one-dimensional Bose gas with repulsive δ-function interactions are found. The calculation depends only on scattering information in the form of two- and three-body scattering wavefunctions. Although not in agreement with a previous calculation by Servadio, our results are shown to be consistent with the work of Yang and Yang which involves the use of periodic rather than scattering boundary conditions.

DOI
10.1063/1.1666499

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Exact expressions for the cluster coefficients b2 and b3 for the one-dimensional Bose gas with repulsive δ-function interactions are found. The calculation depends only on scattering information in the form of two- and three-body scattering wavefunctions. Although not in agreement with a previous calculation by Servadio, our results are shown to be consistent with the work of Yang and Yang which involves the use of periodic rather than scattering boundary conditions.
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We solve the three-boson problem with contact two-and three-body interactions in one dimension and analytically calculate the ground and excited trimer-state energies.Then, by using the diffusion Monte Carlo technique we calculate the binding energy of three dimers formed in a one-dimensional Bose-Bose or Fermi-Bose mixture with attractive interspecies and repulsive intraspecies interactions.Combining these results with our three-body analytics, we extract the three-dimer scattering length close to the dimer-dimer zero crossing.In both considered cases the three-dimer interaction turns out to be repulsive.Our results constitute a concrete proposal for obtaining a one-dimensional gas with a pure three-body repulsion.