Ground State Energy and Momentum Distribution Function for a Bose Gas Within a Multi-Rods Structure

We use the Variational Monte Carlo ({VMC}) method to calculate the ground state (gs) energy and the momentum distribution of an interacting Bose gas confined by a one-dimensional periodic multi-rods structure created by an external Kronig-Penney potential. The VMC gs energy is compared with that previously obtained using the Mean-Field theory approximation by solving analytically the Gross-Pitaevskii equation [1]. In the limit of zero external potential, we recover the well-known Lieb-Liniger gas, which for strong interactions becomes the Tonks gas. In this limit case, we compare our variational results with those obtained originally by Lieb and Liniger [2], as well as with those calculated by means of the Diffusion Monte Carlo ({DMC}) method [3]. Only in the region of high density and weak interaction, Mean-Field results are equal to DMC results and slightly better than the variational ones. [1] O.A. Rodr\'iguez and M.A. Sol\'is, ``Ground state of a Lieb-Liniger gas within multi-rods solving analytically the Gross-Pitaevskii equation", work in process. [2] E.H. Lieb and W. Liniger, PR {\bf 130}, 1605 (1963). [3] G.E. Astrakharchik and S. Giorgini, PRA {\bf 68}, 031602 (2003). We thank partial support from grants CONACyT 221030 and PAPIIT IN107616.