On the Validity of Collective Variable Description of Bose Systems

概要

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The validity of Sunakawa, Yamasaki and Kebukawa's Hamilionian and that of Bogoliubov and Zubarev's Hamiltonian are examined. Perturbational expansion of the ground state energy by these Hamiltonians disagrees with the exact solution of Lieb and Liniger for one-dimensional Bose system with repulsive delta-function interaction. This fact suggests that these Hamiltonians are not microscopic descriptions of the many-Boson system. Mathematical inconsistency in Bogohubov and Zubarev's theory is also pointed out. Moreover analytic expression of high density expansion for the ground state energy density e_0 is found out to be e_0n^<-1>=γ-(4/3π)γ^<3/2>+(1/6-1/π^2)γ^2+Ο(γ^<5/2>), γ≡2/n, for one-dimensional Bose system with delta function interaction (density n, strength 2c, ℏ=2m=1) by the use of the correlated basis function method.
理論物理学刊行会の論文
1975-02-25