2025/02/07 by Hinrichs, Benjamin, Jonas Lampart, Lampart, Jonas +1 · 3 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Chromodynamics and Particle Interactions #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2502.04876
openalex publication_date 2025/02/07 · openalex created_date 2025/02/11 · openalex updated_date 2026/07/28
We study the ultraviolet problem for models of a finite-dimensional quantum mechanical system linearly coupled to a bosonic quantum field, such as the (many-)spin boson model or its rotating-wave approximation. If the state change of the system upon emission or absorption of a boson is either given by a normal matrix or by a 2-nilpotent one, which is the case for the previously named examples, we prove an optimal renormalization result. We complement it, by proving the norm resolvent convergence of appropriately regularized models to the renormalized one. Our method consists of a dressing transformation argument in the normal case and an appropriate interior boundary condition for the 2-nilpotent case.