Stability of topologically protected edge states in nonlinear quantum walks: Additional bifurcations unique to Floquet nonlinear systems. (arXiv:1907.08464v1 [quant-ph])

Quantum walk, a kind of systems with time-periodic driving (Floquet systems),
is defined by a time-evolution operator, and can possess non-trivial
topological phases. Recently, the stability of topologically protected edge
states in a nonlinear quantum walk has been studied, in terms of an effective
time-indepedent non-Hermitian Hamiltonian, by applying a continuum limit to the
nonlinear quantum walk. In this paper, we study the stability of the edge
states by treating a nonunitary time-evolution operator, which is derived from
the time-evolution operator of nonlinear quantum walks without the continuum
limit. As a result, we find additional bifurcations at which edge states change
from stable attractors to unstable repellers with increasing the strength of
nonlinearity. The additional bifurcation we shall show is unique to Floquet
nonlinear systems, since the origin of the bifurcations is that a stable region
for eigenvalues of nonunitary time-evolution operators is bounded, while that
of effective non-Hermitian Hamiltonians is unbouneded.

Article web page: