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

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, ${\sigma }^2\propto t^3$, 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 $\to$ diffusive $\to$ superdiffusive $\to$ ballistic $\to$ 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.

11 pages, 11 figures

References in corpus (43)

• Quantum random walks - an introductory overview
• Quantum algorithms: an overview
• Universal computation by quantum walk
• From quantum cellular automata to quantum lattice gases
• Elephants can always remember: Exact long-range memory effects in a non-Markovian random walk
• Decoherence can be useful in quantum walks
• Higher-Than-Ballistic Conduction of Viscous Electron Flows
• Quantum speedup for active learning agents
• Anomalous diffusion: A basic mechanism for the evolution of inhomogeneous systems
• Open Quantum Random Walks
• Entanglement in coined quantum walks on regular graphs
• Quantum walk on the line: entanglement and non-local initial conditions
• Dynamically Disordered Quantum Walk as a Maximal Entanglement Generator
• Quantum Walks as simulators of neutrino oscillations in vacuum and matter
• Entangling Power of Disordered Quantum Walks
• Universally Optimal Noisy Quantum Walks on Complex Networks
• Degree Distribution in Quantum Walks on Complex Networks
• Efficiency of open quantum walk implementation of dissipative quantum computing algorithms
• The Dirac equation as a quantum walk over the honeycomb and triangular lattices
• Dynamic-Disorder-Induced Enhancement of Entanglement in Photonic Quantum Walks
• Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks
• Two-dimensional quantum walk under artificial magnetic field
• Quantum walks with sequential aperiodic jumps
• Effects of long-range hopping and interactions on quantum walk in ordered and disordered lattices
• The Elephant Quantum Walk
• Environmental engineering for quantum energy transport
• Aperiodic space-inhomogeneous quantum walks: localization properties, energy spectra and enhancement of entanglement
• Enhanced non-Markovian behavior in quantum walks with Markovian disorder
• Fermion confinement via Quantum Walks in 2D+1 and 3D+1 spacetime
• Universal Behavior of Quantum Walks with Long-Range Steps
• Weak disorder enhancing the production of entanglement in quantum walks
• The quantum Levy walk
• Quantum Walk with Jumps
• Quantum walk on a cylinder
• Interacting quantum walkers: Two-body bosonic and fermionic bound states
• On a generalised model for time-dependent variance with long-term memory
• Accelerated quantum walk, two-particle entanglement generation and localization
• Scaling and crossover behaviour in a truncated long range quantum walk
• Long-range memory elementary 1D cellular automata: Dynamics and nonextensivity
• Inhibition of spreading in quantum random walks due to quenched Poisson-distributed disorder
• Unusual scaling in a discrete quantum walk with random long range steps
• Light-cone and local front dynamics of a single-particle extended quantum walk
• Persistent quantum walks: dynamic phases and diverging timescales

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• Quantum walks in two dimensions: controlling directional spreading with entangling coins and tunable disordered step operator
• Discrete-time quantum walk dispersion control through long-range correlations
• Persistent quantum walks: dynamic phases and diverging timescales
• Localization in Quantum Walks with a Single Lattice Defect: A Comparative Study
• Quantum walks with spatiotemporal fractal disorder
• Phase vs coin vs position disorder as a probe for the resilience and revival of single particle entanglement in cyclic quantum walks
• Directionality and quantum backfire in continuous-time quantum walks from delocalized states: Exact results
• Enhanced spreading in continuous-time quantum walks using aperiodic temporal modulation of defects