1210.2596 (Ran Qi et al.)
Ran Qi, Xiwen Guan
We study strong interaction effects in a one-dimensional (1D) Boson gas in a narrow confinement induced resonance (CIR). In contrast to the zero range potential, the 1D two-body interaction potential in the narrow CIR can be written as a polynomial of derivative $\delta$-function interaction on many-body level. In the knowledge of the Bethe ansatz, we show that the low energy physics of this many-body problem is described by the Tomonaga-Luttinger liquid where the Luttinger parameters are essentially modified by the finite range parameter $v$. This parameter drastically changes critical phenomena and thermodynamics of the strongly interacting gas. It remarkably drives the Tonks gas from non-mutual statistics to mutual statistics or to the super Tonks-Girardeau phase. This novel feature is further discussed in terms of the breathing mode which is experimentally measurable.
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http://arxiv.org/abs/1210.2596
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