Close to s-wave Feshbach resonances two and few-atom systems can come near the continuum threshold, and three atoms in the state of zero angular momentum presents the Efimov or Thomas effect when the scattering length is large or the range of the s-wave interaction tends to zero. In this limit the binding energy and sizes of three-body systems in zero angular momentum states are dependent on a three-body single scale, showing universal and model independent correlations between these quantities. In two dimensions the relevant s-wave scales are the pair binding energy, which leads to model independent laws for the dependence of the three-body bound state energies on these quantities. The continuous transition between these different scaling behaviors in three-boson systems by continuously squeezing one dimension will be also discussed. The four-boson system in 3 dimensions in the limit of s-wave zero range forces exhibits a scaling behavior with a new single scale, which appears, in particular, in the position of the four-body resonant recombination. Range correction to this scaling law will be shown and results compared to the experimental data.
