2023/07/27 by Marcel Griesemer, V. Kußmaul, Griesemer, M. +1
Mathematics · #81Q99 #81V10 (Primary) 35J10 (Secondary) #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2307.14986
openalex publication_date 2023/07/27 · openalex created_date 2023/07/29 · openalex updated_date 2026/07/28
Kato's well known distributional inequality for the magnetic Laplacian holds equally in the more general setting of non-relativistic quantum electrodynamics (QED), where the wave function is vector-valued and the vector potential is quantized. We give two new applications of this result: First, we show that eigenstates satisfy a subsolution estimate. Second, for general states, with energy distribution strictly below the ionization threshold, we give a short proof of pointwise exponential decay in the electronic configuration.