Nonlinear flip-flop quantum walks through potential barriers

The dynamics of nonlinear flip-flop quantum walk with amplitude-dependent phase shifts pertubing potential barrier is investigated. Through the adjustment between uniform local perturbations and a Kerr-like nonlinearity medium we find rich set dynamic profiles. We will show existence different Hadamard walking regimes, including those mobile soliton-like structures or self-trapped states. latter predominant for amplitudes that tend to $\ensuremath{\varphi}\ensuremath{\rightarrow}\ensuremath{\pi}/2$. In this system, qubit shows an unusual behavior as increase barriers displays monotonic decrease in self-trapping ${\ensuremath{\varphi}}_{c}$ respect parameter. A chaotic-like regime becomes intermediate values. Furthermore, that, by changing coins ($\ensuremath{\theta}$) nontrivial arises, where close Pauli-$X$ drives system structures, while chaotic are restricted narrow region $\ensuremath{\chi}\ensuremath{-}\ensuremath{\varphi}$ plane. believe possible implement observe proprieties model integrated photonic system.