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 [1], passing to a system with finite energies in the Born-Oppenheimer (BO) approximation [2] and finishing with a general system [3]. 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 the effective dimension.

Emergence of N-Body Tunable Interactions in Universal Few-Atom Systems

“…However, it still missing systematic experimental studies about the effect of the dimensional change in few-body observables, e.g., the Efimov effect is drastically affected by the spatial dimensional reduction. The disappearance of Efimov effect in fractional dimensions between three and two dimensions, including another few-body aspects involving a continuous change of spatial dimensions, has recently being investigated by some groups [26,[30][31][32][33][34][35][36].…”