# Dimensional effects in Efimov physics

## TL;DR

This paper reviews recent theoretical advances on how the Efimov effect, a quantum phenomenon in three-boson systems, is influenced by the spatial dimension, highlighting the role of effective potentials and dimensionality in its occurrence.

## Contribution

It provides a comprehensive review of the effects of dimensionality on Efimov physics using various theoretical approaches, including zero-range potentials and the Born-Oppenheimer approximation.

## Key findings

- Efimov states exist in 3D but not in 2D or 1D.
- The effective potential's form is proportional to 1/R^2 and its strength determines the Efimov effect.
- Dimensionality influences the critical conditions for Efimov state formation.

## 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, passing to a system with finite energies in the Born-Oppenheimer (BO) approximation and finishing with a general system. 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.