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

Ken Mochizuki, Norio Kawakami, Hideaki Obuse

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number085702
JournalJournal of Physics A: Mathematical and Theoretical
Volume53
Issue number8
DOIs
Publication statusPublished - 2020 Jan 29
Externally publishedYes

Keywords

  • bifurcations
  • nonlinear effects
  • periodically driven systems (Floquet systems)
  • quantum walks
  • topologically protected edge states

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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