2017/09/30 by Giuseppe Di Molfetta, Diogo O. Soares-Pinto, Silvio M. Duarte Queiros +1
Computer Science · Mathematics · Physics and Astronomy · #Exponent #Lattice (music) #Markov process #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum and electron transport phenomena #Quantum dynamics #Quantum mechanics #Quantum process #Quantum walk #Random walk #Statistical physics #Statistics #cs.CC #quant-ph
paper · pdf · doi:10.1103/physreva.97.062112
published as Phys. Rev. A 97, 062112 (2018) · 4 figures, any comments is welcome. Accepted in PRA
arxiv created 2018/06/01 · openalex publication_date 2018/06/13 · arxiv updated 2018/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 \ensuremathσt2 grows cubicly with time \ensuremathσ\ensuremath∝t3. 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.