期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
卷 38, 期 7, 页码 3687-3703出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2018159
关键词
Quantum walks; scattering theory; dispersive estimates; Strichartz estimates; nonlinear scattering
资金
- JSPS KAKENHI [JP15K17568, JP17H02851, JP17H02853, JP17K05311, JP26800054]
- Japan Society for the Promotion of Science [16K17637, 16K03939]
- JSPS [26400156]
- Grants-in-Aid for Scientific Research [26400156, 16K03939, 26800054, 16K17637] Funding Source: KAKEN
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 Schrodinger equations and discrete nonlinear Schrodinger equations but it seems to be the first time to be applied to QWs.
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