Efimov effect in a <i>D</i>-dimensional Born–Oppenheimer approach

Rosa, D. S.; Frederico, T.; Krein, G.; Yamashita, M. T.

doi:10.1088/1361-6455/aaf346

Cited by 12 publications

(7 citation statements)

References 27 publications

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“…In this work, we considered particles with equal masses and the same interactions between them. It would be interesting to apply the same framework to massimbalanced systems [97][98][99][100]. Moreover, if we consider interactions with different scattering lengths between the pairs, we would have three instead of a single a value and also different effective ranges.…”

Section: Discussionmentioning

confidence: 99%

Quantum Monte Carlo studies of a trimer scaling function with microscopic two- and three-body interactions

Madeira,

Frederico,

Gandolfi

et al. 2021

Preprint

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We present an energy scaling function to predict, in a specific range, the energy of bosonic trimers with large scattering lengths and finite range interactions, which is validated by quantum Monte Carlo calculations using microscopic Hamiltonians with two-and three-body potentials. The proposed scaling function depends on the scattering length, effective range, and a reference energy, which we chose as the trimer energy at unitarity. We obtained the scaling function as a limit cycle from the solution of the renormalized zero-range model with effective range corrections. We proposed a simple parameterization of the energy scaling function. Besides the intrinsic interest in theoretical and experimental investigations, this scaling function allows one to probe Efimov physics with only the trimer ground-states, which may open opportunities to identify Efimov trimers whenever access to excited states is limited.

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Section: Discussionmentioning

confidence: 99%

Quantum Monte Carlo studies of a trimer scaling function with microscopic two- and three-body interactions

Madeira,

Frederico,

Gandolfi

et al. 2021

Preprint

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“…Note that an imaginary s means the loss of scale invariance in Eqs. (1) and (2). However, this does not give the physical reason for the existence of an Efimov state.…”

Section: The Ideal Case: No Physical Scalesmentioning

confidence: 90%

“…In Section 3 we show the physical reason for the disappearance of Efimov states [2]. We use the BO approximation to generalize the result from Fonseca, Redish and Shanley [20] and obtain the effective potential in D dimensions for AAB systems, which is responsible for the fall to the center phenomenon that generates the infinite number of three-body bound states.…”

Section: Introductionmentioning

confidence: 95%

“…This discussion will be made in this section with a less ideal situation: the physical scales are now present, but there is a condition for A. Part of the content of this section was published in [2]. In the Landau and Lifshitz book on nonrelativistic quantum mechanics [24], one can read: "to reveal certain properties of quantum-mechanical motion it is useful to examine a case which, it is true, has no direct physical meaning: the motion of a particle in a field where the potential energy becomes infinite at some point (the origin) according to the law U (r) ∼ −β/r 2 (β > 0)".…”

Section: A Less Ideal Case: Three-body System In the Born-oppenheimermentioning

confidence: 99%

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Dimensional Effects in Efimov Physics

Yamashita

2019

Few-Body Syst

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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 [1], passing to a system with finite energies in the Born-Oppenheimer (BO) approximation [2] and finishing with a general system [3]. 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.

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“…However, it still missing systematic experimental studies about the effect of the dimensional change in few-body observables, e.g., the Efimov effect is drastically affected by the spatial dimensional reduction. The disappearance of Efimov effect in fractional dimensions between three and two dimensions, including another few-body aspects involving a continuous change of spatial dimensions, has recently being investigated by some groups [26,[30][31][32][33][34][35][36].…”

Section: Introduction -An Overview Of Recent Problems Involving Universality In Few-body Systemsmentioning

confidence: 99%

Emergence of N-Body Tunable Interactions in Universal Few-Atom Systems

2020

Self Cite

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A three-atom molecule AAB, formed by two identical bosons A and a distinct one B, is studied by considering coupled channels close to a Feshbach resonance. It is assumed that the subsystems AB and AA have, respectively, one and two channels, where, in this case, AA has open and closed channels separated by an energy gap. The induced three-body interaction appearing in the single channel description is derived using the Feshbach projection operators for the open and closed channels. An effective three-body interaction is revealed in the limit where the trap setup is tuned to vanishing scattering lengths. The corresponding homogeneous coupled Faddeev integral equations are derived in the unitarity limit. The s-wave transition matrix for the AA subsystem is obtained with a zero-range potential by a subtractive renormalization scheme with the introduction of two finite parameters, besides the energy gap. The effect of the coupling between the channels in the coupled equations is identified with the energy gap, which essentially provides an ultraviolet scale that competes with the van der Waals radius-this sets the short-range physics of the system in the open channel. The competition occurring at short distances exemplifies the violation of the "van der Waals universality" for narrow Feshbach resonances in cold atomic setups. In this sense, the active role of the energy gap drives the short-range three-body physics.

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Efimov effect in a D-dimensional Born–Oppenheimer approach

Cited by 12 publications

References 27 publications

Quantum Monte Carlo studies of a trimer scaling function with microscopic two- and three-body interactions

Quantum Monte Carlo studies of a trimer scaling function with microscopic two- and three-body interactions

Dimensional Effects in Efimov Physics

Emergence of N-Body Tunable Interactions in Universal Few-Atom Systems

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