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

Abstract : Abstract 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, σ 2 ∝ t 3 , 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 leads to multiple transitions between dynamical regimes, namely ballistic → diffusive → superdiffusive → ballistic → hyperballistic for non-hermitian coin whereas the first diffusive regime is quelled for implementations using the Hadamard coin. In addition, we observe a robust asymptotic approach to maximal coin-space entanglement.
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https://hal-amu.archives-ouvertes.fr/hal-03594736
Contributor : Giuseppe Di Molfetta Connect in order to contact the contributor
Submitted on : Wednesday, March 2, 2022 - 7:30:37 PM
Last modification on : Thursday, March 3, 2022 - 3:38:07 AM

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Di Molfetta Giuseppe, Marcelo Pires, Giuseppe Di Molfetta, Sílvio Queirós. Multiple transitions between normal and hyperballistic diffusion in quantum walks with time-dependent jumps. Scientific Reports, Nature Publishing Group, 2019, 9 (1), pp.19292. ⟨10.1038/s41598-019-55642-5⟩. ⟨hal-03594736⟩

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