2015/09/28 by Benjamin Landon, Jane Panangaden, Landon, Benjamin +5
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Spectroscopy and Quantum Chemical Studies #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1509.08525
arxiv created 2015/09/28 · openalex publication_date 2015/09/28 · arxiv updated 2015/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The dynamic reflection probability and the spectral reflection probability for a one-dimensional Schroedinger operator H = - Δ+ V are characterized in terms of the scattering theory of the pair (H, H_∞) where H_∞ is the operator obtained by decoupling the left and right half-lines ℝ≤ 0 and ℝ≥ 0. An immediate consequence is that these reflection probabilities are in fact the same, thus providing a short and transparent proof of the main result of Breuer, J., E. Ryckman, and B. Simon (2010) . This approach is inspired by recent developments in non-equilibrium statistical mechanics of the electronic black box model and follows a strategy parallel to the Jacobi case.