发表机构
İzmir Institute of Technology; Boğaziçi University（伊兹密尔理工大学; 博阿齐奇大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对具纯离散未受扰谱的量子系统，构建含时点相互作用的微扰框架，推导极点位移等物理量，经多示例验证且可简化为标准含时微扰理论。
AI 中文摘要
我们为具有纯离散未受扰谱的量子系统中的含时点相互作用构建了微扰框架。在二维和三维中，点相互作用通过热核正则化得到的重整化预解式描述，而在一维中，对角格林函数是有限的，无需重整化。时间相关性通过相互作用参数或支撑点的运动引入。在两种情况下，我们都将非自治哈密顿量按对应静态点相互作用问题的谱基展开，并推导了一阶和二阶极点位移、投影修正及跃迁振幅。该方法通过具体示例说明：含时耦合的点相互作用、受运动点相互作用微扰的谐振子、球面上带有运动相互作用中心的粒子。我们还讨论了带有运动δ势的一维谐振子，表明在非重整化情形下，该公式可简化为标准含时微扰理论。
英文摘要
We develop a perturbative framework for time-dependent point interactions in quantum systems with purely discrete unperturbed spectrum. In two and three dimensions the point interaction is described through the renormalized resolvent obtained from heat-kernel regularization, while in one dimension the diagonal Green function is finite and no renormalization is required. Time dependence is introduced either through the interaction parameter or through the motion of the support point. In both cases we expand the non-autonomous Hamiltonian in the spectral basis of the corresponding static point-interaction problem and derive the first- and second-order pole shifts, projection corrections, and transition amplitudes. We also describe how finite degeneracies are treated by separating the coupled point-interaction direction from the unaffected orthogonal subspace in each degenerate eigenspace. The method is illustrated by explicit examples: point interactions with time-dependent coupling, harmonic oscillators perturbed by moving point interactions, and a particle on a sphere with a moving interaction center. We also discuss the one-dimensional harmonic oscillator with a moving delta potential, showing that in the non-renormalized case the present formulation reduces to the standard time-dependent perturbation theory. Finally, an exactly solvable delta center moving with constant velocity on a circle is used as a discrete-spectrum example for the local moving-center expansion and its velocity-dependent dynamical corrections.
Comments55 pages, 1 figure, typos are corrected, title has been changed, some domain issues are clarified
Journal refAnnals of Physics 495 170747 (2026)
