Multiple transitions between normal and hyperballistic diffusion in quantum walks with time-dependent jumps

@article{Pires2019MultipleTB,
  title={Multiple transitions between normal and hyperballistic diffusion in quantum walks with time-dependent jumps},
  author={Marcelo A. Pires and Giuseppe Di Molfetta and S'ilvio M. Duarte Queir'os},
  journal={Scientific Reports},
  year={2019},
  volume={9}
}
We extend to the gamut of functional forms of the probability distribution of the time-dependent step-length a previous model dubbed Elephant Quantum Walk, which considers a uniform distribution and yields hyperballistic dynamics where the variance grows cubicly with time, σ2 ∝ t3, and a Gaussian for the position of the walker. We investigate this proposal both locally and globally with the results showing that the time-dependent interplay between interference, memory and long-range hopping… 
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