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 Schrödinger equations and discrete nonlinear Schrödinger equations but it seems to be the first time to be applied to QWs.
|Number of pages||17|
|Journal||Discrete and Continuous Dynamical Systems- Series A|
|Publication status||Published - 2018 Jul|
- Dispersive estimates
- Nonlinear scattering.
- Quantum walks
- Scattering theory
- Strichartz estimates
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics