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We show that self-localized ground states can be created in the spin-balancedgas of fermions with repulsion between the spin components, whose strengthgrows from the center to periphery, in combination with the harmonic-oscillator(HO) trapping potential acting in one or two transverse directions. We alsoconsider the ground state in the non-interacting Fermi gas under the action ofthe spatially growing tightness of the one- or two-dimensional (1D or 2D) HOconfinement. These settings are considered in the framework of theThomas-Fermi-von Weizsacker (TF-vW) density functional. It is found that the vWcorrection to the simple TF approximation (the gradient term) is nearlynegligible in all situations. The properties of the ground state under theaction of the 2D and 1D HO confinement with the tightness growing in thetransverse directions is investigated too for the Bose-Einstein condensate(BEC) with the self-repulsive nonlinearity.

Self-trapping of Fermi and Bose gases under spatially modulated repulsive nonlinearity and transverse confinement