Stability of topologically protected edge states in nonlinear quantum walks: Additional bifurcations unique to Floquet systems

Ken Mochizuki, Norio Kawakami, Hideaki Obuse

研究成果: Article査読

3 被引用数 (Scopus)

抄録

Recently, effects of nonlinearity on topologically nontrivial systems have attracted attention and the stability of topologically protected edge states has been studied for a quantum walk with nonlinear effects, which is akin to time-periodically driven systems (Floquet systems). In the previous work, it has been found that the edge states can be stable attractors or unstable repellers depending on their intrinsic topological property, while the stability is not affected by the strength of nonlinearity. In the present work, we find additional bifurcations at which edge states change from stable attractors to unstable repellers with increasing the strength of nonlinearity in nonlinear quantum walks, for the first time. The new bifurcations are unique to Floquet systems, since we take dynamical properties of Floquet systems into consideration by directly applying the time-evolution operator of the quantum walks to the linear stability analysis. Our results shed new light on nonlinear effects on topological edge states in Floquet systems.

本文言語English
論文番号085702
ジャーナルJournal of Physics A: Mathematical and Theoretical
53
8
DOI
出版ステータスPublished - 2020 1 29
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 統計学および確率
  • モデリングとシミュレーション
  • 数理物理学
  • 物理学および天文学(全般)

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