Near-threshold behavior of the ground-state binding energies of the few-atom systems of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow /><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow /><mml:mrow /></mml:mmultiscripts></mml:mrow></mml:math>and other bosons in two and three dimensions

Lim, T. K.; Nakaichi, S.; Akaishi, Yoshinori; Tanaka, Hajime

doi:10.1103/physreva.22.28

Cited by 18 publications

(24 citation statements)

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“…The fits for N = 4 − 7 predict critical masses m (N ) * /m He between 0.62 and 0.63, which agree within their uncertainties with those predicted for N = 2 and 3. Our analysis thus confirms that the critical mass m (N ) * at which 2D systems, interacting additively through a given two-body potential, become unbound is the same for all system sizes [10,11,12].…”

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confidence: 71%

“…Figure 1 shows clear deviations from a linear behavior, indicating that the term proportional to (m−m (2) * ) 2 cannot be neglected for N = 2. Earlier studies [10,11,12] did not see deviations from the linear behavior possibly because the total ground state energies were i) varied over a smaller range, and ii) determined variationally. The qualitative behavior of the energies calculated using the KORONA and the LJ potential is similar, which implies that the non-linear behavior cannot be attributed to the difference in the long-range parametrization of the two two-body potentials [the LJ potential is for large r proportional to r −6 , while the KORONA potential contains additional terms proportional to r −j , where…”

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confidence: 99%

“…This critical mass is predicted to be universal, i.e., m (N ) * = m * [10], and to be the same for the corresponding homogeneous system [8,19]. ii) For a given system size, the ground state energies E N near threshold are predicted to change exponentially as the atomic mass m decreases [7,11]. Similarly, for a given atomic mass, the ground state energies near threshold are predicted to change exponentially with varying system size [17].…”

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confidence: 99%

“…Effectively 2D atom traps have been realized recently [5,6]; extension to optical lattices with only a few atoms per lattice site is possible with today's technology. These systems are particularly interesting since Feshbach resonances allow the interaction strengths to be tuned through application of magnetic fields.Bosonic 2D systems interacting through short-range two-body potentials that support one zero angular momentum bound state are predicted to exhibit intriguing universal, that is, model-independent, behaviors [7,8,9,10,11,12,13,14,15,16,17,18]. i) 2D clusters with N particles [9,10,12] are predicted to become unbound when the mass m reaches a critical value m (N ) * [7].…”

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confidence: 99%

“…This paper reports the energetics of self-bound inhomogeneous 2D systems near threshold, and tests under which conditions predictions i) to iii) apply. To this end we perform numerical many-body calculations, which supersede earlier variational calculations [10,11] and cover a wider parameter range. For N = 2 and 3 we determine the ground state energy using basis set expansiontype calculations.…”

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Threshold behavior of bosonic two-dimensional few-body systems

Blume

2005

Phys. Rev. B

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Bosonic two-dimensional self-bound clusters consisting of N atoms interacting through additive van der Waals potentials become unbound at a critical mass m (N) * ; m (N) * has been predicted to be independent of the size of the system. Furthermore, it has been predicted that the ground state energy EN of the N -atom system varies exponentially as the atomic mass approaches m * . This paper reports accurate numerical many-body calculations that allow these predictions to be tested. We confirm the existence of a universal critical mass m * , and show that the near-threshold behavior can only be described properly if a previously neglected term is included. We comment on the universality of the energy ratio EN+1/EN near threshold. PACS numbers:Restricting the motion of particles to one or two dimensions can lead to properties that differ dramatically from those in three dimensions. The most prominent two-dimensional (2D) system is the surface of bulk matter. Another example are one-or two-atom layer thin films, e.g., atomic or molecular hydrogen films [1,2], grown on substrates. Neglecting the adatom-substrate interaction, many properties of such systems can be understood within a truly 2D framework. In addition to homogeneous 2D systems, it is interesting to consider 2D clusters (see, e.g., Refs. [3,4]). What happens when a finite number of atoms is restricted to 2D space? Inhomogeneous 2D systems can potentially be studied by placing a few atoms on the surface of a substrate or by confining atoms by external potentials. Effectively 2D atom traps have been realized recently [5,6]; extension to optical lattices with only a few atoms per lattice site is possible with today's technology. These systems are particularly interesting since Feshbach resonances allow the interaction strengths to be tuned through application of magnetic fields.Bosonic 2D systems interacting through short-range two-body potentials that support one zero angular momentum bound state are predicted to exhibit intriguing universal, that is, model-independent, behaviors [7,8,9,10,11,12,13,14,15,16,17,18]. i) 2D clusters with N particles [9,10,12] are predicted to become unbound when the mass m reaches a critical value m (N ) * [7]. This critical mass is predicted to be universal, i.e., m (N ) * = m * [10], and to be the same for the corresponding homogeneous system [8,19]. ii) For a given system size, the ground state energies E N near threshold are predicted to change exponentially as the atomic mass m decreases [7,11]. Similarly, for a given atomic mass, the ground state energies near threshold are predicted to change exponentially with varying system size [17]. iii) The ratio between the ground state energies of a 2D system with N +1 atoms and those of a system with N atoms reaches, in the limit of zero-range interactions, a constant. This constant has been determined analytically for small 2D systems: E δ 3 /E δ 2 = 16.52 [9,16] and E δ 4 /E δ 3 = 11.94 [18]. For large systems, the ratio E δ N +1 /E δ N has been predicted to approach 8.57 [17]...

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confidence: 71%

mentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

mentioning

confidence: 99%

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Threshold behavior of bosonic two-dimensional few-body systems

Blume

2005

Phys. Rev. B

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The Fonseca-Redish-Shanley solvable model for a molecular three-body system and the efimov effect in two dimensions

Lim

Shimer

1980

Z Physik A

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We have applied the Fonseca-Redish-Shanley solvable model for three bodies, two heavy and one light, in two dimensions for two types of Yamaguchi form factors in order to determine if the Efimov Effect exists there. The long-range effective heavy-heavy interaction which we extract in each case does not support an infinite number of bound states. Our results therefore indicate that the effect does not manifest itself in two dimensions.

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Universal Properties of the Four-Boson System in Two Dimensions

2004

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Abstract. We consider the nonrelativistic four-boson system in two dimensions interacting via a short-range attractive potential. For a weakly attractive potential with one shallow two-body bound state with binding energy B 2 , the binding energies B N of shallow N -body bound states are universal and thus do not depend on the details of the interaction potential. We compute the fourbody binding energies in an effective quantum mechanics approach. There are exactly two bound states: the ground state with B Introduction.-Low-dimensional systems are ubiquitous in many areas of physics. In condensed matter physics, e.g., they are of interest in connection with high-T c superconductivity and the Quantum Hall effect. A two-dimensional boson system has been realized experimentally with hydrogen adsorbed on a helium surface [1]. The experimental progress with ultracold atomic gases and BoseEinstein Condensates has made it possible to engineer low-dimensional atomic systems in anisotropic traps [2,3,4].This experimental progress has also stimulated theoretical activities. Recently, the problem of N weakly attractive bosons in two spatial dimensions (2D) was revisited [5]. Relying on the asymptotic freedom of nonrelativistic bosons in 2D with attractive short-range interactions, some surprising universal properties of self-bound N -boson droplets were predicted for N ≫ 1. In particular, the size R N of the N -boson droplets was found to decrease exponentially with N :

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Near-threshold behavior of the ground-state binding energies of the few-atom systems ofHe4and other bosons in two and three dimensions

Cited by 18 publications

References 14 publications

Threshold behavior of bosonic two-dimensional few-body systems

Threshold behavior of bosonic two-dimensional few-body systems

The Fonseca-Redish-Shanley solvable model for a molecular three-body system and the efimov effect in two dimensions

Universal Properties of the Four-Boson System in Two Dimensions

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