Communications in Mathematical Physics

, Volume 156, Issue 1, pp 101–126 | Cite as

The Efimov effect. Discrete spectrum asymptotics

  • A. V. Sobolev


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.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • A. V. Sobolev
    • 1
    • 2
  1. 1.Département de Mathématiques et InformatiqueUniversité Paris-NordVilletaneuseFrance
  2. 2.St-Petersburg Branch of the Steklov Institute (SPOMI)St-PetersburgRussia

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