# 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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