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.KT2024
Trace formula and Levinson's theorem as an index pairing in the presence of resonances
Angus Alexander
We realise the number of bound states of a Schrödinger operator on as an index pairing in all dimensions. Expanding on ideas of Guillopé and others, we use high-ener…
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…