Efimov's Effect: A New Pathology of Three-Particle Systems. II

Amado, R. D.; Noble, J.V.

doi:10.1103/physrevd.5.1992

Cited by 135 publications

(108 citation statements)

References 4 publications

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“…Это соотношение верно, если ε = J/(48c − 5), где c = T 3 ds 1 ds 2 ds 3 9 + cos s 1 + cos s 2 + cos s 3 .…”

Section: двухмагнонное состояниеunclassified

“…Этот эффект впервые был обнаружен Ефимовым [1]. В работах [2], [3] эта задача изучалась в физическом аспекте. Строгое математическое доказательство существования эффекта Ефимова было проведено впервые в работе [4], а затем в работах [5]- [7].…”

Section: Introductionunclassified

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О Спектре Оператора Энергии Двухмагнонных Систем В Трехмерной Изотропной Примесной Ферромагнитной Модели Гейзенберга

Tashpulatov¹

2010

ТМФ

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“…Это соотношение верно, если ε = J/(48c − 5), где c = T 3 ds 1 ds 2 ds 3 9 + cos s 1 + cos s 2 + cos s 3 .…”

Section: двухмагнонное состояниеunclassified

Section: Introductionunclassified

О Спектре Оператора Энергии Двухмагнонных Систем В Трехмерной Изотропной Примесной Ферромагнитной Модели Гейзенберга

Tashpulatov¹

2010

ТМФ

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“…As discussed in Ref. [7] this occurs not only for identical particles, a situation first considered by Efimov [8][9][10], but also for two identical and one different particle. In particular, in the case of two heavy particles and one light particle these authors found that the heavyheavy interaction does not matter, and there is an infinite number of bound trimer states as long as the light-heavy scattering length becomes infinite.…”

mentioning

confidence: 95%

“…The authors thank Dr. M. Bhattacharya for helpful discussions, and Dr. P. Julienne for bringing Ref. [7] to their attention. * Electronic address: pierre.meystre@optics.arizona.edu…”

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confidence: 99%

Coherent Atom-Trimer Conversion in a Repulsive Bose-Einstein Condensate

2007

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We show that the use of a generalized atom-molecule dark state permits the enhanced coherent creation of triatomic molecules in a repulsive atomic Bose-Einstein condensate, with further enhancement being possible in the case of heteronuclear trimers via the constructive interference between two chemical reaction channels.PACS numbers: 03.75. Pp, 03.70.+k The experimental realization of Bose-Einstein condensates (BEC) in dilute atomic vapors has led to a number of spectacular advances with implications well past the confines of traditional atomic, molecular and optical (AMO) physics [1], and with profound relevance for fields ranging from condensed matter physics to quantum information science. A development of particular relevance for the present study is the generation and probing of ultracold molecular samples and of molecular condensates from atomic BEC, using magnetic Feshbach resonances (FR) and photoassociation (PA) [2-6] to control the dynamics of the system. In particular, it has recently been shown that these two techniques can be combined to achieve the efficient and stable conversion of atoms into molecular dimers [3].The goal of this paper is to demonstrate theoretically that these techniques can in principle be extended to the generation of molecular trimers. An important new result is that the creation of heteronuclear trimers can be significantly enhanced by the constructive interference of two quantum channels leading to their formation from a two-component atomic condensate. The basic idea is to first create highly excited dimers via a standard FR, and then to couple them to a bound trimer via PA. A key element of the scheme is to exploit a coherent population trapping (CPT) technique to prevent the dimer population from becoming significant throughout the conversion process. Such a scheme has previously been proposed for the creation of molecular dimers [3], and has been theoretically demonstrated to be stable for a broad range of conditions. This proposed extension of "superchemistry" [6] manipulations from dimers to trimers exploits the existence of three-body bound states in ultracold atomic samples as the scattering length for two-body collisions becomes infinite. As discussed in Ref. [7] this occurs not only for identical particles, a situation first considered by Efimov [8-10], but also for two identical and one different particle. In particular, in the case of two heavy particles and one light particle these authors found that the heavyheavy interaction does not matter, and there is an infinite number of bound trimer states as long as the light-heavy scattering length becomes infinite. In the case of the interaction between one heavy and two light particles, by contrast, there is no infinite number of bound states unless both two-body scattering lengths become simultaneously infinite.We mentioned that a point of particular interest in the formation of heteronuclear trimers A 2 B is the role of quantum interferences between the two paths that involve intermediate dimers A 2 (path AA) a...

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“…We can find the domain equation by combining (12) and (13). Together, as Λ → ∞, these equations impose the following conditions on wavefunctions:…”

Section: Renormalizing the Three-body Problemmentioning

confidence: 99%

Renormalized contact potential in two dimensions

Henderson

Rajeev

1998

Journal of Mathematical Physics

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We obtain for the attractive Dirac δ-function potential in twodimensional quantum mechanics a renormalized formulation that avoids reference to a cutoff and running coupling constant. Dimensional transmutation is carried out before attempting to solve the system, and leads to an interesting eigenvalue problem in N −2 degrees of freedom (in the center of momentum frame) when there are N particles. The effective Hamiltonian for N − 2 particles has a nonlocal attractive interaction, and the Schrodinger equation becomes an eigenvalue problem for the logarithm of this Hamiltonian. The 3-body case is examined in detail, and in this case a variational estimate of the ground-state energy is given.

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Efimov's Effect: A New Pathology of Three-Particle Systems. II

Cited by 135 publications

References 4 publications

О Спектре Оператора Энергии Двухмагнонных Систем В Трехмерной Изотропной Примесной Ферромагнитной Модели Гейзенберга

О Спектре Оператора Энергии Двухмагнонных Систем В Трехмерной Изотропной Примесной Ферромагнитной Модели Гейзенберга

Coherent Atom-Trimer Conversion in a Repulsive Bose-Einstein Condensate

Renormalized contact potential in two dimensions

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