Semiclassical scattering amplitude at the maximum point of the potential
Ivana Alexandrova, Jean-Francois Bony, Thierry Ramond
TL;DR
This paper calculates the semiclassical scattering amplitude at a potential maximum energy level, extending previous work by analyzing trapped trajectories using advanced mathematical frameworks.
Contribution
It introduces a novel analysis of trapped trajectories in semiclassical scattering at a potential maximum, building on and extending prior theoretical methods.
Findings
Explicit formula for scattering amplitude at maximum point
Analysis of trapped trajectories' contribution
Extension of previous semiclassical scattering results
Abstract
We compute the scattering amplitude for Schr\"odinger operators at a critical energy level, corresponding to the maximum point of the potential. We follow the wrok of Robert and Tamura, '89, using Isozaki and Kitada's representation formula for the scattering amplitude, together with results from Bony, Fujiie, Ramond and Zerzeri '06 in order to analyze the contribution of trapped trajectories.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Quantum chaos and dynamical systems · Quantum Mechanics and Non-Hermitian Physics