The 1D interacting Bose gas in a hard wall box

Details The 1D interacting Bose gas in a hard wall box The 1D interacting Bose gas in a hard wall box

2005-05-23

arxiv.org/abs/cond-mat/0505550v3

J. Phys. A 38 (2005) 7787-7806

Physics

Condensed Matter

Statistical Mechanics

23 pages, 7 figures. Improved version. Extra figure added for the weak coupling regime. New expression for the interaction-dep

Scientific paper

10.1088/0305-4470/38/36/001

We consider the integrable one-dimensional delta-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 coupling 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.

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