Scattering and inverse scattering for nonlinear quantum walks

Masaya Maeda, Hironobu Sasaki, Etsuo Segawa, Akito Suzuki, Kanako Suzuki

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

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 Schrödinger equations and discrete nonlinear Schrödinger equations but it seems to be the first time to be applied to QWs.

Original languageEnglish
Pages (from-to)3687-3703
Number of pages17
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume38
Issue number7
DOIs
Publication statusPublished - 2018 Jul

Keywords

  • Dispersive estimates
  • Nonlinear scattering.
  • Quantum walks
  • Scattering theory
  • Strichartz estimates

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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