SMALL CLUSTERS OF PURE AND ADMIXED H↑,<sup>3</sup>He↑, T↑, AND<sup>4</sup>He ATOMS

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

doi:10.1051/jphyscol:1980731

Cited by 5 publications

(15 citation statements)

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“…However, these potentials of finite size with k 1 R s ≫ 1 behave qualitatively different from the potential in eq. (9). In this limit it is again possible to reduce eq.…”

Section: Square Well With Barrier or Corementioning

confidence: 99%

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Occurrence conditions for two-dimensional Borromean systems

et al. 2013

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We search for Borromean three-body systems of identical bosons in two dimensional geometry, i.e. we search for bound three-boson system without bound two-body subsystems. Unlike three spatial dimensions, in two-dimensional geometry the two-and three-body thresholds often coincide ruling out Borromean systems. We show that Borromean states can only appear for potentials with substantial attractive and repulsive parts. Borromean states are most easily found when a barrier is present outside an attractive pocket. Extensive numerical search did not reveal Borromean states for potentials without an outside barrier. We outline possible experimental setups to observe Borromean systems in two spatial dimensions. PACS. 03.65.Ge Solutions of wave equations: bound states -67.85.-d Ultracold gases, trapped gases -36.20.-r Macromolecules and polymer molecules 2 Two-body problem in two dimensionsAccording to the definition Borromean states, if they exist, appear for two-body potentials at the edge of two-body

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“…However, these potentials of finite size with k 1 R s ≫ 1 behave qualitatively different from the potential in eq. (9). In this limit it is again possible to reduce eq.…”

Section: Square Well With Barrier or Corementioning

confidence: 99%

“…The thresholds for binding of two and three-body systems are identical and Borromean structures cannot exist. Moreover, numerical investigations in momentum space [6,7] and coordinate space [8,9,10,11,12,13] revealed that in 2D some other classes of potentials have no Borromean states.…”

Section: Introductionmentioning

confidence: 99%

Occurrence conditions for two-dimensional Borromean systems

et al. 2013

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“…Several other approaches have been used for few-body systems of atoms interacting via the contact interaction. Among these are effective field theory approaches [25,26,27,28], shell-model [29,30], and Monte Carlo calculations [31,32,33] in three dimensions for fermions, various hyperspherical and variational approaches in three [34,35,36,37,38] and in two dimensions for bosons [39,40,41,42], and exact diagonalization in two dimensions for fermions [43,44] and for bosons [44]. The zerorange interaction does not allow the diagonalization of the many-body Hamiltonian in spatial dimensions greater than one, so all these methods must address that in some way.…”

Section: Bosons Interacting In a Trapmentioning

confidence: 99%

Analytic harmonic approach to theN-body problem

Armstrong

Zinner

Fedorov

et al. 2011

J. Phys. B: At. Mol. Opt. Phys.

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We consider an analytic way to make the interacting N -body problem tractable by using harmonic oscillators in place of the relevant two-body interactions. The two-body terms of the N -body Hamiltonian are approximated by considering the energy spectrum and radius of the relevant two-body problem which gives frequency, center position, and zero point energy of the corresponding harmonic oscillator. Adding external harmonic one-body terms, we proceed to solve the full quantum mechanical N -body problem analytically for arbitrary masses. Energy eigenvalues, eigenmodes, and correlation functions like density matrices can then be computed analytically. As a first application of our formalism, we consider the N -boson problem in two-and three dimensions where we fit the two-body interactions to agree with the well-known zerorange model for two particles in a harmonic trap. Subsequently, condensate fractions, spectra, radii, and eigenmodes are discussed as function of dimension, boson number N , and scattering length obtained in the zero-range model. We find that energies, radii, and condensate fraction increase with scattering length as well as boson number, while radii decrease with increasing boson number. Our formalism is completely general and can also be applied to fermions, Bose-Fermi mixtures, and to more exotic geometries.

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“…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].…”

mentioning

confidence: 96%

“…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%

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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SMALL CLUSTERS OF PURE AND ADMIXED H↑,³He↑, T↑, AND⁴He ATOMS

Cited by 5 publications

References 0 publications

Occurrence conditions for two-dimensional Borromean systems

Occurrence conditions for two-dimensional Borromean systems

Analytic harmonic approach to theN-body problem

Threshold behavior of bosonic two-dimensional few-body systems

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SMALL CLUSTERS OF PURE AND ADMIXED H↑,3He↑, T↑, AND4He ATOMS

Cited by 5 publications

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Occurrence conditions for two-dimensional Borromean systems

Occurrence conditions for two-dimensional Borromean systems

Analytic harmonic approach to theN-body problem

Threshold behavior of bosonic two-dimensional few-body systems

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Resources

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SMALL CLUSTERS OF PURE AND ADMIXED H↑,³He↑, T↑, AND⁴He ATOMS