Multiparticle Interactions of Zero-Range Potentials

Macek, J. H.

doi:10.1007/s00601-009-0026-7

Cited by 8 publications

(3 citation statements)

References 7 publications

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“…The well may produce three body resonances corresponding to trapping of all three particles in a potential barrier. Thus, in addition to Efimov bound states, there can also be Efimov resonances [21]. Calculations using model two-body potentials actually find such resonances [22].…”

Section: C7mentioning

confidence: 97%

Efimov states: what are they and why are they important?

Macek

2007

Phys. Scr.

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The interaction of two atoms at energies in the microkelvin range is mainly characterized by one parameter, namely, the s-wave scattering length. Efimov showed that when the scattering length was effectively infinite, i.e. much larger than the natural length scale of the atoms, a large number of three-body bound states could form even when the two-body system supported only one weakly bound state, or possibly none at all. The states are bound in an effective 1/R2 potential and therefore form a series with a characteristic energy spacing. These states are called Efimov states and are conceptually important since they indicate a new way to form aggregates of particles. They bear some relation to vibrationally bound states of three atoms. The theory of these states and their relation to vibrational binding is reviewed in light of recent experimental measurements.

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Section: C7mentioning

confidence: 97%

Efimov states: what are they and why are they important?

Macek

2007

Phys. Scr.

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“…In either case, zero-range potentials are useful when the details of the interaction at small distances are not critical for the dynamics. The description of Bose condensates is an example in which zero-range interactions are fundamental to theories of the condensed aggregates [31].…”

Section: Introductionmentioning

confidence: 99%

Puiseux series expansion for an eigenvalue of the generalized Friedrichs model with perturbation of rank 1

Lakaev¹,

Darus²,

Kurbanov³

2013

J. Phys. A: Math. Theor.

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A family Hμ(p), μ > 0, of the generalized Friedrichs model with perturbation of rank 1, associated with a system of two particles, moving on the one-dimensional lattice is considered. The existence of a unique eigenvalue E(μ, p), of the operator Hμ(p) lying below the essential spectrum is proved. For any p from a neighborhood of the origin, the Puiseux series expansion for eigenvalue E(μ, p) at the point μ = μ(p) ⩾ 0 is found. Moreover, the asymptotics for E(μ, p) is established as μ → +∞.

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“…The debate on the theoretical evidences of the short-range four-body scales on real systems, as in cold atom traps, is underway (see e.g. [1,3,[5][6][7][8][9][10][11][12][13][14]).…”

mentioning

confidence: 99%

Universality in Four-Boson Systems

Frederico,

Delfino,

Hadizadeh

et al. 2012

Preprint

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We report recent advances on the study of universal weakly bound four-boson states from the solutions of the Faddeev-Yakubovsky equations with zero-range two-body interactions. In particular, we present the correlation between the energies of successive tetramers between two neighbor Efimov trimers and compare it to recent finite range potential model calculations. We provide further results on the large momentum structure of the tetramer wave function, where the four-body scale, introduced in the regularization procedure of the bound state equations in momentum space, is clearly manifested. The results we are presenting confirm a previous conjecture on a four-body scaling behavior, which is independent of the three-body one. We show that the correlation between the positions of two successive resonant four-boson recombination peaks are consistent with recent data, as well as with recent calculations close to the unitary limit. Systematic deviations suggest the relevance of range corrections.

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Multiparticle Interactions of Zero-Range Potentials

Cited by 8 publications

References 7 publications

Efimov states: what are they and why are they important?

Efimov states: what are they and why are they important?

Puiseux series expansion for an eigenvalue of the generalized Friedrichs model with perturbation of rank 1

Universality in Four-Boson Systems

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