Dimensional Effects in Efimov Physics

Abstract

Efimov physics is drastically affected by the change of spatial dimensions. Efimov states occur in a tridimensional (3D) environment, but disappear in two (2D) and one (1D) dimensions. In this paper, dedicated to the memory of Prof. Faddeev, we will review some recent theoretical advances related to the effect of dimensionality in the Efimov phenomenon considering three-boson systems interacting by a zero-range potential. We will start with a very ideal case with no physical scales (Rosa et al. in Phys Rev A 97:050701, 2018), passing to a system with finite energies in the Born–Oppenheimer (BO) approximation (Rosa et al. in J Phys B At Mol Opt Phys 52:025101, 2018) and finishing with a general system (Sandoval et al. in J Phys B At Mol Opt Phys 51:065004, 2018). The physical reason for the appearance of the Efimov effect is given essentially by two reasons which can be revealed by the BO approximation—the form of the effective potential is proportional to 1 / R 2 (R is the relative distance between the heavy particles) and its strength is smaller than the critical value given by - (D- 2) 2 / 4 , where D is effective dimension.