Efimov effect evaporation after confinement

Abstract

The continuous confinement of quantum systems can be described by means of the d-method, where the dimension d is taken as a continuous parameter. In this work we describe in detail how this method can be used to obtain the root mean square radii for a squeezed three-body system. These observables are used to investigate the disappearance of the Efimov states around the two-body threshold during a progressive confinement of the system from three to two dimensions. We illustrate how the disappearance takes place through the loss of one of the particles, whereas the other two remain bound.Introduction. The properties of few-body systems are to a large extent determined by the dimension of the space where they are allowed to move. The simplest example is perhaps the case of a two-body system, always bound in two dimensions (2D) by any infinitesimally small attractive potential, but not necessarily bound in three dimensions (3D) due to the different behavior of the centrifugal barrier [1,2]. This fact has two immediate consequences. The first one is that the Efimov effect, present in three-body systems where at least two of the three pair-interactions have nearly zero energy [3], does not exist in 2D [4,5,6,7,8]. The second one is that, when confining an unbound two-body system from 3D to 2D, there must necessarily be a point in the confinement process where the two-body system is precisely at the zero-energy threshold.From this last result one can also conclude that, given an unbound threebody system containing at least two identical particles, when confining from 3D to 2D there will always be a point in the confinement process where the Efimov This work has been partially supported by the Spanish Ministry of Science, Innovation and University MCIU/AEI/FEDER,UE (Spain) under Contract No. PGC2018-093636-B-I00.