Universal dynamical scaling laws in three-state quantum walks

We perform a finite-time scaling analysis over the detrapping point of a three-state quantum walk on the line. The coin operator is parametrized by rho that controls the wave packet spreading velocity. The input state prepared at the origin is set as a symmetric linear combination of two eigenstates of the coin operator with a characteristic mixing angle theta, one of them being the component that results in full spreading occurring at theta(c)(rho) for which no fraction of the wave packet remains trapped near the initial position. We show that relevant quantities, such as the survival probability and the participation ratio assume single parameter scaling forms at the vicinity of the detrapping angle theta(c). In particular, we show that the participation ratio grows linearly in time with a logarithmic correction, thus, shedding light on previous reports of sublinear behavior.

Automated summary

In this study, a finite-time scaling analysis was performed over the detrapping point of a three-state quantum walk on the line. It was found that relevant quantities such as survival probability and participation ratio exhibit single parameter scaling forms near the detrapping angle. Particularly, the participation ratio grows linearly in time with a logarithmic correction, providing insight into previous reports of sublinear behavior.