M T Batchelor et al 2005 J. Phys. A: Math. Gen. 38 7787 doi:10.1088/0305-4470/38/36/001
M T Batchelor1,2, X W Guan1,2, N Oelkers1,2 and C Lee3,4
Show affiliationsWe consider the integrable one-dimensional δ-function interacting Bose gas in a hard wall box which is exactly solved via the coordinate Bethe ansatz. The ground-state energy, including the surface energy, is derived from the Lieb–Liniger-type integral equations. The leading and correction terms are obtained in the weak and strong coupling regimes from both the discrete Bethe equations and the integral equations. This allows the investigation of both finite-size and boundary effects in the integrable model. We also study the Luttinger liquid behaviour by calculating Luttinger parameters and correlations. The hard wall boundary conditions are seen to have a strong effect on the ground-state energy and phase correlations in the weak coupling regime. Enhancement of the local two-body correlations is shown by application of the Hellmann–Feynman theorem.
71.10.Pm Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.)
82B23 Exactly solvable models; Bethe ansatz
Quantum gases, liquids and solids
Issue 36 (9 September 2005)
Received 24 May 2005
Published 23 August 2005
M T Batchelor et al 2005 J. Phys. A: Math. Gen. 38 7787
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