Asymptotic distribution of negative eigenvalues for three-body systems in two dimensions: Efimov effect in the antisymmetric space

The [Formula: see text]-wave resonances induce an infinite number of negative eigenvalues accumulating at the origin for the system of three identical particles in two dimensions, provided that the energy operator is restricted on the subspace of wave functions which are antisymmetric with respect to the permutations. This quantum phenomenon is called the super Efimov effect and corresponds to the Efimov effect in three dimensions. It has been predicted in physics literature [ 10 ] and a mathematical proof has been given by Gridnev [ 5 ]. In this paper, we prove this effect for a wider class of pair interactions and improve the results obtained by [ 5 ]. We do not necessarily assume that the interactions are radially symmetric, have a definite signature and fall off exponentially at infinity. The essence of the proof is put in the asymptotic analysis of the singular behavior at low energy for resolvents of the Schrödinger operators with [Formula: see text]-wave resonances at zero energy.

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