2015/08/31 by Andrea Mantile, Mantile, Andrea
Mathematics · Physics and Astronomy · #35B40 #35Q41 #37B55 #81Q12 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DS #math.MP #msc:35B40 #msc:35Q41 #msc:37B55 #msc:81Q12
paper · pdf · doi:10.48550/arxiv.1508.07737
Latex; 20 pages. arXiv admin note: substantial text overlap with arXiv:1503.07701
arxiv created 2015/08/31 · arxiv updated 2015/09/01
We consider a class of modified Schroedinger operators where the semiclassical Laplacian is perturbed with h-dependent interface conditions occurring at the boundaries of the potential's support. Under positivity assumptions on the potential, we show that this modification produces a small perturbation on the dynamics as h->0, independently from the time scale. In the case of a time dependent potential, this yields uniform-in-h stability estimates for products of instantaneous propagators. Then, following a standard approach, the non-autonomous dynamical system is defined as a limit of stepwise propagators and its small-h expansion is provided under suitable regularity assumptions on the potential's variations.