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Di Molfetta, G., Soares-Pinto, D. O., & Duarte Queiros, S. M. (2018). Elephant quantum walk. Phys. Rev. A, 97(6), 062112–6pp.
Abstract: 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 sigma(2)(t) grows cubicly with time sigma alpha 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.
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