Continuous-time quantum walks in the presence of a quadratic perturbation
Continuous-time quantum walks in the presence of a quadratic perturbation
We address the properties of continuous-time quantum walks with Hamiltonians of the form $\mathcal{H}=L+\ensuremath{\lambda}{L}^{2}$, with $L$ the Laplacian matrix of the underlying graph and the perturbation $\ensuremath{\lambda}{L}^{2}$ motivated by its potential use to introduce next-nearest-neighbor hopping. We consider cycle, complete, and star graphs as paradigmatic models with low and high …