Efimov Effect Evaporation After Confinement

Garrido, E.; Jensen, A. S.

doi:10.1007/s00601-021-01613-4

Cited by 4 publications

(4 citation statements)

References 13 publications

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“…The strength of the open and closed channels, V o and V c in Eq. (11), are fixed in order to reproduce, respectively, the value of a open , known experimentally, and a closed as given in Eq. (49) for d = 3.…”

Section: Constructing the Two-body Potentialsmentioning

confidence: 99%

“…This is the hallmark of appearance of the Efimov effect. The properties and behavior of the Efimov states for arbitrary d, and how they appear and disappear in the vicinity of d = d E are investigated in [6,11]. Under these conditions the details of the short-distance two-body potentials play a very minor role, and the physics has therefore a universal character.…”

Section: Introductionmentioning

confidence: 99%

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

Garrido

Jensen

2021

Physics Letters A

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Section: Constructing the Two-body Potentialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Garrido

Jensen

2021

Physics Letters A

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“…Finally, the coupling strength, V co in Eq. (11), is obtained by imposing that, for B = B 0 and d = 3, we must get a tw = ∞.…”

Section: Constructing the Two-body Potentialsmentioning

confidence: 99%

“…This is the hallmark of appearance of the Efimov effect. The properties and behavior of the Efimov states for arbitrary d, and how they appear and disappear in the vicinity of d = d E are investigated in [6,11]. Under these conditions the details of the shortdistance two-body potentials play a very minor role, and the physics has therefore a universal character.…”

Section: Introductionmentioning

confidence: 99%

Tuning of Efimov states in non-integer dimensions

Garrido

Jensen

2023

Eur. Phys. J. D

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The purpose of this paper is to show that, by combining Feshbach resonances with external confining potentials, the energy scale factor of neighboring Efimov states can be tremendously reduced. The Efimov conditions can be reached for systems made of three different particles. For the case of two identical light particles and a heavy particle, the energy factor can be reduced by many orders of magnitude, and the Efimov states are in this way more easily reachable experimentally. The equivalence between external potentials and the formulation in terms of non-integer dimensions, d, is exploited. The technically simpler d-method is used to derive analytic expressions for two-component relative wave functions describing two short-range square-well interacting particles. The two components express one open and one closed channel. The scattering length is obtained after phase shift expansion, providing an analytic form for the Efimov condition. We illustrate the results by means of systems made of $$^7$$ 7 Li, $$^{39}$$ 39 K, and $$^{87}$$ 87 Rb, with realistic parameters. The related pairs of dimension and magnetic field are shown and discussed. The results are universal as they only rely on large-distance properties. Graphic abstract

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Confinement of N-Body Systems and Non-integer Dimensions

Garrido,

Jensen

2024

Few-Body Syst

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The squeezing process of a three-dimensional quantum system by use of an external deformed one-body oscillator potential can also be described by the d-method, without external field and where the dimension can take non-integer values. In this work we first generalize both methods to N particles and any transition between dimensions below 3. Once this is done, the use of harmonic oscillator interactions between the particles allows complete analytic solutions of both methods, and a direct comparison between them is possible. Assuming that both methods describe the same process, leading to the same ground state energy and wave function, an analytic equivalence between the methods arises. The equivalence between both methods and the validity of the derived analytic relation between them is first tested for two identical bosons and for squeezing transitions from 3 to 2 and 1 dimensions, as well as from 2 to 1 dimension. We also investigate the symmetric squeezing from 3 to 1 dimensions of a system made of three identical bosons. We have in all the cases found that the derived analytic relations between the two methods work very well. This fact permits to relate both methods also for large squeezing scenarios, where the brute force numerical calculation with the external field is too much demanding from the numerical point of view, especially for systems with more than two particles.

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Efimov Effect Evaporation After Confinement

Cited by 4 publications

References 13 publications

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

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

Tuning of Efimov states in non-integer dimensions

Confinement of N-Body Systems and Non-integer Dimensions

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