Dimensional Effects in Efimov Physics
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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.
This work was partly supported by funds provided by the Brazilian agencies Fundação de Amparo à Pesquisa do Estado de São Paulo—FAPESP Grants No. 2016/01816-2, Conselho Nacional de Desenvolvimento Científico e Tecnológico—CNPq Grant No. 302075/2016-0(MTY), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—CAPES Grant No. 88881.030363/2013-01. I would like to especially thank my collaborators D.S. Rosa, J.H. Sandoval, T. Frederico and G. Krein for all discussions during the development of the articles reported in this review.
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