Non-autonomous quantum systems with scale-dependent interface conditions
Abstract
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.
Cite
@article{arxiv.1508.07737,
title = {Non-autonomous quantum systems with scale-dependent interface conditions},
author = {Andrea Mantile},
journal= {arXiv preprint arXiv:1508.07737},
year = {2015}
}
Comments
Latex; 20 pages. arXiv admin note: substantial text overlap with arXiv:1503.07701