Elephant quantum walk
Giuseppe Di Molfetta, Diogo O. Soares-Pinto, Sı́lvio M. Duarte Queirós · Physical Review A · 2018
We introduce an analytically treatable discrete time quantum walk in a one-dimensional lattice which combines non-Markovianity and hyperballistic diffusion associated with a Gaussian whose variance ${\ensuremath{\sigma}}_{t}^{2}$ grows cubicly with time $\ensuremath{\sigma}\ensuremath{\propto}{t}^{3}$. These properties have have been numerically found in several systems, namely, tight-binding lattice models. For its rules, our model can be understood as the quantum version of the classical non-Markovian ``elephant random walk'' process for which the quantum coin operator only changes the value of the diffusion constant although, contrarily, to the classical coin.