Bogoliubov-like mode in the Tonks-Girardeau Gas

Details Bogoliubov-like mode in the Tonks-Girardeau Gas Bogoliubov-like mode in the Tonks-Girardeau Gas

2005-02-25

arxiv.org/abs/cond-mat/0502600v1

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, 1 figure

Scientific paper

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: $\omega(q)=q \sqrt{\bar\rho U(q)/m}$, where $\bar\rho$ is the bosons density and $U(q)$ is a Fourier component of the two-body potential.

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