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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 p…
math-ph2025
Topological Levinson's theorem and corrections at thresholds: the full picture in a quasi-1D example
T. T. Nguyen, D. Parra, S. Richard
Various threshold effects are investigated on a discrete quasi-1D scattering system. In particular, one of these effects is to add corrections to Levinson's theorem. We explain how…
math-ph2024
Discrete time scattering and Wold's decomposition in pictures
Rafi Rizqy Firdaus, Serge Richard
Based on explicit computations, various concepts of discrete time scattering theory are reviewed, discussed, and illustrated. The dynamics are taking place on a discrete half-space…