Communications in Mathematical Physics

, Volume 156, Issue 1, pp 101–126

The Efimov effect. Discrete spectrum asymptotics

  • A. V. Sobolev

DOI: 10.1007/BF02096734

Cite this article as:
Sobolev, A.V. Commun.Math. Phys. (1993) 156: 101. doi:10.1007/BF02096734


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.

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
  3. 3.Department of MathematicsUniversity of TorontoTorontoCanada

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