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Bogoliubov-like mode in the Tonks-Girardeau Gas

Igor V. Ovchinnikov·Daniel Neuhauser
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Abstract

We reformulate 1D boson-fermion duality in path-integral terms. The result is a 1D counterpart of the boson-fermion duality in the 2D Chern-Simons gauge theory. The theory is consistent and enables, using standard resummation techniques, to obtain the long-wave-length asymptotics of the collective mode in 1D boson systems at the Tonks-Girardeau regime. The collective mode has the dispersion of Bogoliubov phonons: $ω(q)=q \sqrt{\barρU(q)/m}$, where $\barρ$ is the bosons density and $U(q)$ is a Fourier component of the two-body potential.

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Igor V. Ovchinnikov, Daniel Neuhauser. 2005-02-25. Bogoliubov-like mode in the Tonks-Girardeau Gas. https://arxiv.org/abs/cond-mat/0502600

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