Excitatio Spectrum of a One-dimensional Many-Boson System
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概要
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The lowest order correction term to the Bogoliubov spectrum is calculated analytically for the case of one-dimensional bosons with δ-function interaction. We obtain the spectrum ε(p)=？p？√<p^2+4nc> + (2nc/π)γ^<1/2>・？p？/√<p^2+4nc> + O(γnc), (n=density, ℏ=2m=1, strength of δ-function = 2c, γ=c/n). This is compared with Lieb's exact excitation spectrum for this case. Our numerical calculation shows that it is the correct γ^<1/2> expansion of the spectrum. However this expansion up to second order is not a good approximation for the low wave number part and gives an incorrect expansion of the sound velocity up to second order.
- 理論物理学刊行会の論文
- 1976-01-25
著者
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Takahashi Minoru
Department Of Appied Physics Tohoku University
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Takahashi Minoru
Department Of Physics College Of General Education Osaka University
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