Elephant quantum walk

摘要

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 σ_t~2 grows cubicly with time σ ∝ 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.