2006/03/31 by Denis D. Sheka, Franz G. Mertens · 5 citations
Mathematics · Physics and Astronomy · #Aharonov–Bohm effect #Bound state #Geometry #Gravitational singularity #Magnetic field #Mathematical physics #Mathematics #Nonlinear system #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #Quantum mechanics #Scattering #Soliton #Square (algebra) #quant-ph
paper · pdf · doi:10.1103/physreva.74.052703
published in Physical Review A 74(5) (American Physical Society) · 5 pages (REVTeX)
arxiv created 2006/09/25 · openalex publication_date 2006/11/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We apply the recently generalized Levinson theorem for potentials with inverse-square singularities [Sheka et al., Phys. Rev. A 68, 012707 (2003)] to Aharonov-Bohm systems in two dimensions (2D). By this theorem, the number of bound states in a given mth partial wave is related to the phase shift and the magnetic flux. The results are applied to 2D soliton-magnon scattering.