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.

中文翻译：

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二维三体系统负特征值的渐近分布：反对称空间中的 Efimov 效应

[公式：见正文]-波共振会在二维三个相同粒子系统的原点处产生无限数量的负特征值，前提是能量算子被限制在相对于反对称的波函数的子空间中到排列。这种量子现象被称为超级艾菲莫夫效应，对应于三个维度的艾菲莫夫效应。它已在物理学文献 [10] 中预测，Gridnev [5] 给出了数学证明。在本文中，我们证明了这种效应适用于更广泛的配对交互，并改进了 [5] 获得的结果。我们不一定假设相互作用是径向对称的，具有明确的特征并且在无穷远处呈指数下降。