2025/12/09 by Ballesteros, Miguel, Cordova, Gerardo Franco, Schulz-Baldes, Hermann
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics
paper · doi:10.48550/arxiv.2512.08335
openalex publication_date 2025/12/09 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28
The boundary value of the resolvent of a generic periodic tight-binding Hamiltonian with matrix symbols is shown to satisfy a limit absorption principle which is continuous in energy in dimensions d=3, and in dimension d=2 away from critical points of the energy bands corresponding to van Hove singularities. The analysis away from critical points of the energy bands is based on the coarea formula, while at the critical points it involves a parametric Morse lemma and stationary phase arguments. In particular, at Weyl points a new type of oscillatory integrals is dealt with.