On nonlinear scattering for quantum walks
Mathematical Physics
2017-11-08 v2 Analysis of PDEs
math.MP
Quantum Physics
Abstract
We study large time behavior of quantum walks (QW) with self-dependent 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) QW such as Strichartz estimate. Such argument is standard in the study of nonlinear Schr\"odinger equations but it seems to be the first time to be applied to QW. We also numerically study the dynamics of QW and observe soliton like solutions.
Cite
@article{arxiv.1711.00620,
title = {On nonlinear scattering for quantum walks},
author = {Masaya Maeda and Hironobu Sasaki and Etsuo Segawa and Akito Suzuki and Kanako Suzuki},
journal= {arXiv preprint arXiv:1711.00620},
year = {2017}
}
Comments
23 pages, 7 figures