3 papers
math-ph2025
Levinson's theorem for dissipative systems, or how to count the asymptotically disappearing states
A. Alexander, J. Faupin, S. Richard
We consider dissipative Schroedinger operators of the form on , with a complex, bounded and decaying potential with a non-positive imaginary pa…
math-ph2024
Spectral flow and Levinson's theorem for Schrö dinger operators
Angus Alexander, Adam Rennie
We use spectral flow to present a new proof of Levinson's theorem for Schrödinger operators on with smooth compactly supported potential. Our proof is valid in all d…
math.SP2023
Levinson's theorem for two-dimensional scattering systems: it was a surprise, it is now topological!
A. Alexander, D. T. Nguyen, A. Rennie +1
We prove a general Levinson's theorem for Schrödinger operators in two dimensions with threshold obstructions at zero energy. Our results confirm and simplify earlier seminal resul…