Abstract
In this article we discuss the accuracy of effective one-dimensional (1D) theories used to describe the behavior of ultracold atomic ensembles confined in quantum wires by a harmonic trap. We derive, within a fully many-body approach, the effective Hamiltonian describing this class of systems and we calculate the beyond-mean-field corrections to the energy of the ground state arising from virtual transitions towards the excited state of the confining potential. We find that, due to the Pauli principle, effective finite-range corrections are one order of magnitude larger than effective three-body interactions. By comparing to exact solutions of the purely 1D problem, we conclude that a 1D effective theory provides a good description of the ground state of the system for a rather large range of interaction parameters.
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