Higher order solutions of Lieb-Liniger integral equation |
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Authors: | Toshiaki Kaminaka Miki Wadati |
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Institution: | Department of Physics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan |
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Abstract: | We study higher order solutions of Lieb-Liniger integral equation for a one-dimensional δ-function Bose gas. By use of the power series expansion method, the integral equation is solved and the correction terms which improve the Bogoliubov theory are calculated analytically in the weak coupling regime. Physical quantities such as the ground state energy and the chemical potential are represented by a dimensionless parameter γ=c/ρ, where c is the interaction strength and ρ is the number density of particles while the quasi-momentum distribution function is expressed in terms of a dimensionless parameter λ=c/K, where K is the cut-off momentum. |
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Keywords: | δ-Function Bose gas One-dimensional integrable systems Bethe ansatz method Lieb-Liniger integral equation |
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