The dynamics of an atom waveguide X-junction beam splitter becomes truly one dimensional in a regime of low temperatures and densities and large positive scattering lengths where the transverse mode becomes frozen and the many-body Schr\"odinger dynamics becomes exactly soluble via a generalized Fermi-Bose mapping theorem. We analyze the interferometric response of a double-X-junction interferometer of this type due to potential differences between the interferometer arms.
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Girardeau et al. (2002) studied this question.
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