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

## TL;DR

This paper investigates how increasing nonlinearity causes new bifurcations in topologically protected edge states of Floquet quantum walks, revealing unique dynamical behaviors not seen in static systems.

## Contribution

It uncovers additional bifurcations in nonlinear Floquet quantum walks where edge states transition from stable to unstable, a phenomenon absent in non-Floquet systems.

## Key findings

- Identification of bifurcations caused by nonlinearity in Floquet systems
- Edge states can switch stability with increasing nonlinearity
- Unique bifurcation phenomena specific to Floquet dynamics

## 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.