In a previous work of 2014 on a quantum system governed by the repulsive Hamiltonian, the author proved uniqueness for short-range interactions described by a scattering operator consisting of regular and singular parts. In this paper, the singular part is assumed to have much stronger singularities and the same uniqueness theorem is proved. By applying the time-dependent method invented by Enss and Weder in 1995, the high-velocity limit for a wider class of the scattering operator with stronger singularities also uniquely determines the interactions of a multi-dimensional system.
Asymptotics of the IDS for Schrödinger operators with singular potentials and Gibbs point processes
Graduate School of Human and Environmental Studies, Kyoto University（京都大学研究生院人文与环境研究科）
研究了具有单点势V（essinf V = -∞）的随机Schrödinger算子的积分态密度（IDS）N(E)的渐进行为，假设底层点过程为具有排斥双体相互作用的Gibbs点过程，通过周期近似方法确定了E→-∞时log N(E)的主导项，表明排斥双体相互作用导致N(E)衰减速度比Poisson情况更快，且多簇配置在Gibbs设定中对IDS有主导贡献，与Poisson模型中单簇主导的情况形成对比，还给出了特定势类的主导常数的精细化估计。
