临界情况下的二体阈谱分析
Two-body threshold spectral analysis, the critical case
摘要：
本文研究了具有径向对称势的二维$d$ -维薛定谔算子的一维$d\geq2$低能谱和散射渐近性质，如$-γr^{-2},\;γ>0$。我们考虑角动量扇区，标记为$l=0,1,\dots$，其中$γ>(l+d/2-1)^2$。在每一个这样的扇区中，约化薛定谔算子有无穷多个负本征值累积到零。我们发现，预解有一个非平凡的振荡行为的频谱参数接近零的锥有界远离负半轴，我们推导出一个渐近公式的相移。
英文摘要：
We study in dimension $d\geq2$ low-energy spectral and scattering asymptotics for two-body $d$-dimensional Schrödinger operators with a radially symmetric potential falling off like $-γr^{-2},\;γ>0$. We consider angular momentum sectors, labelled by $l=0,1,\dots$, for which $γ>(l+d/2-1)^2$. In each such sector the reduced Schrödinger operator has infinitely many negative eigenvalues accumulating at zero. We show that the resolvent has a non-trivial oscillatory behaviour as the spectral parameter approaches zero in cones bounded away from the negative half-axis, and we derive an asymptotic formula for the phase shift.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
