Multi-parameter Perturbations of the Laplacian and Resonance Near a Simple Embedded Eigenvalue

Hemant Bansal; Alok Maharana; Lingaraj Sahu

Multi-parameter Perturbations of the Laplacian and Resonance Near a Simple Embedded Eigenvalue

Spectral Theory 2026-06-26 v1 Mathematical Physics

Authors: Hemant Bansal , Alok Maharana , Lingaraj Sahu

Abstract

This paper continues the study of resonance phenomena initiated in [3] for rank-one perturbations. We consider finite-rank multi-parameter perturbations $H_\alpha$ of the Laplacian on $L^2(\mathbb{R}^3)$ and establish Breit--Wigner-type asymptotics for the spectral density of $H_\alpha$ along the resonance $\lambda(\alpha)$ near a simple embedded eigenvalue $\lambda_0$ of $H_a$ as $\alpha\to a$ . We also obtain similar asymptotic behaviour for the scattering cross-section and the average time delay.

Keywords

laplacian perturbations resonance embedded eigenvalue spectral density scattering cross-section time delay breit-wigner asymptotics

Cite

@article{arxiv.2606.28263,
  title  = {Multi-parameter Perturbations of the Laplacian and Resonance Near a Simple Embedded Eigenvalue},
  author = {Hemant Bansal and Alok Maharana and Lingaraj Sahu},
  journal= {arXiv preprint arXiv:2606.28263},
  year   = {2026}
}