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The Efimov effect. Discrete spectrum asymptotics

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Abstract

We study a three-particle Schrödinger operatorH for which none of the two-particle subsystems has negative bound states and at least two of them have zero energy resonances. We prove that under this condition the numberN(z) of bound states ofH belowz<0 has the asymptotics\(N(z) \sim \mathfrak{A}_0 |\log |z||\) asz→-0, where the coefficient\(\mathfrak{A}_0 \) depends only on the ratio of masses of the particles.

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Author notes

  1. A. V. Sobolev

    Present address: Department of Mathematics, University of Toronto, M5S 1A1, Toronto, Canada

Authors and Affiliations

  1. Département de Mathématiques et Informatique, Université Paris-Nord, 93430, Villetaneuse, France

    A. V. Sobolev

  2. St-Petersburg Branch of the Steklov Institute (SPOMI), 191011, St-Petersburg, Russia

    A. V. Sobolev

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  1. A. V. Sobolev
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Communicated by B. Simon

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Sobolev, A.V. The Efimov effect. Discrete spectrum asymptotics. Commun.Math. Phys. 156, 101–126 (1993). https://doi.org/10.1007/BF02096734

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  • DOI: https://doi.org/10.1007/BF02096734

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