Resonances as Viscosity Limits for Exterior Dilation Analytic Potentials

2020/02/28 by Haoren Xiong, Xiong, Haoren
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2002.12490

openalex publication_date 2020/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For exterior dilation analytic potential, V, we use the method of complex scaling to show that the resonances of - Δ+ V , in a conic neighbourhood of the real axis, are limits of eigenvalues of - Δ+ V - i εx² as ε→ 0+ , if V can be analytically extended from ℝⁿ to a truncated cone in ℂⁿ.

Citations

• Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter\n spaces
• A class of analytic perturbations for one-body Schrödinger Hamiltonians

Related

• Scattering resonances as viscosity limits
• Outgoing solutions via Gevrey-2 properties
• Resonances for non-analytic potentials
• Locating resonances on hyperbolic cones
• An example of resonance instability