Efimov effect in non-integer dimensions induced by an external field

Garrido, E.; Jensen, A. S.

doi:10.1016/j.physleta.2020.126982

Cited by 11 publications

(34 citation statements)

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“…In Ref. [9] it is also shown (Fig. 5 in [9]) that, when squeezing to dimensions smaller than d E , the three lowest Efimov states survive as bound three-body states down to d = 2 [14].…”

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confidence: 94%

“…This fact has recently been investigated in Ref. [9], where the confinement of the unbound three-body state was implemented by using the dimension d as a parameter that moves continuously from d = 3 to d = 2, in such a way that for some particular value, d = d E , the Efimov effect shows up. One of the main results in [9] is that the Efimov states appear and disappear around the two-body threshold extremely fast within a very small dimension interval around d = d E .…”

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confidence: 99%

“…The results will be illustrated with one of the systems detailed in Ref. [9], namely the case of two heavy and one light particles with mass ratio m H /m L = 133/6, and with heavy-light potential such that d E = 2.75.…”

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confidence: 99%

“…Therefore, along the squeezing process, from three to two dimensions, the heavy-light system unavoidably becomes bound for some particular strength of the external squeezing potential, or, equivalently, within the d-formalism, for some specific value of the non-integer dimension, d = d E . For this dimension, d E , the two-body binding energy is equal to zero, and, since only relative s-waves are considered, the Efimov conditions are fulfilled [9].…”

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confidence: 99%

“…In here we shall use the heavy-light Gaussian potential specified in Ref. [9] (the range of the potential is taken as length unit), which determines the appearance of the Efimov states for d = d E = 2.75. We shall consider the mass ratio m H /m L = 133/6, which, as shown in [9], corresponds to an energy scale factor between the Efimov states of 46.5.…”

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confidence: 99%

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Efimov effect evaporation after confinement

Garrido

Jensen

2021

Preprint

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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.

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“…In Ref. [9] it is also shown (Fig. 5 in [9]) that, when squeezing to dimensions smaller than d E , the three lowest Efimov states survive as bound three-body states down to d = 2 [14].…”

mentioning

confidence: 94%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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