Scattering and inverse scattering for nonlinear quantum walks
Mathematical Physics
2018-01-31 v2 Analysis of PDEs
math.MP
Abstract
We study large time behavior of quantum walks (QWs) with self-dependent (nonlinear) coin. In particular, we show scattering and derive the reproducing formula for inverse scattering in the weak nonlinear regime. The proof is based on space-time estimate of (linear) QWs such as dispersive estimates and Strichartz estimate. Such argument is standard in the study of nonlinear Schr\"odinger equations and discrete nonlinear Schr\"odinger equations but it seems to be the first time to be applied to QW.
Cite
@article{arxiv.1801.03214,
title = {Scattering and inverse scattering for nonlinear quantum walks},
author = {Masaya Maeda and Hironobu Sasaki and Etsuo Segawa and Akito Suzuki and Kanako Suzuki},
journal= {arXiv preprint arXiv:1801.03214},
year = {2018}
}
Comments
18 pages, text overlap with arXiv:1711.00620