Tuned oscillatory behavior in discrete quantum walks on star clusters

Abstract

A discrete time quantum walk on the star network is considered, on which the walker has a waiting probability at any time step and for any of the $N$ nodes. This contrasts with a previous continuous time analysis, in which the walker in any of the $N\ensuremath{-}1$ leaf nodes is forced to jump back to the central hub. The model amounts to considering two coin operators, one for the hub (with $N$ possible states) and another one for all leaf nodes (with two possible states). The solution depends on $N$ and $\ensuremath{\theta}$, an angle gauging the action of the coin operator on the leaf nodes. Periodic solutions are identified, which can be represented as superposition of large-period branches, sharing a relative small number of shapes and displaced by a regular interval. It is shown that the large period is very sensitive to the choice of $N$ and $\ensuremath{\theta}$. The possibility of experimental applications of this property is briefly mentioned.