2024/08/06 by T. J. Christiansen, Christiansen, T. J., Kiril Datchev +3
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2408.03233
openalex publication_date 2024/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compute low energy asymptotics for the resolvent of the Aharonov--Bohm Hamiltonian with multiple poles for both integer and non-integer total fluxes. For integral total flux we reduce to prior results in black-box scattering while for non-integral total flux we build on the corresponding techniques using an appropriately chosen model resolvent. The resolvent expansion can be used to obtain long-time wave asymptotics for the Aharonov--Bohm Hamiltonian with multiple poles. An interesting phenomenon is that if the total flux is an integer then the scattering resembles even-dimensional Euclidean scattering, while if it is half an odd integer then it resembles odd-dimensional Euclidean scattering. The behavior for other values of total flux thus provides an `interpolation' between these.