Generalized Quantum Walk in Momentum Space
arXiv:quant-ph/0408183 · doi:10.1016/j.physa.2005.01.026
Abstract
We consider a new model of quantum walk on a one-dimensional momentum space that includes both discrete jumps and continuous drift. Its time evolution has two stages; a Markov diffusion followed by localized dynamics. As in the well known quantum kicked rotor, this model can be mapped into a localized one-dimensional Anderson model. For exceptional (rational) values of its scale parameter, the system exhibits resonant behavior and reduce to the usual discrete time quantum walk on the line.
11 pages, 5 figures
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- Nonlinear optical Galton board
- Entangling Power of Disordered Quantum Walks
- Asymptotic behavior of quantum walks with spatio-temporal coin fluctuations
- Distribution of chirality in the quantum walk: Markov process and entanglement
- Driving quantum walk spreading with the coin operator
- Neutrino oscillations in discrete-time quantum walk framework
- Tailoring discrete quantum walk dynamics via extended initial conditions: Towards homogeneous probability distributions
- Localized quantum walks as secured quantum memory
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- Quantum random walks using quantum accelerator modes
- Optical implementability of the two-dimensional Quantum Walk
- Sub-ballistic behavior in quantum systems with Lévy noise
- Quantum walks: decoherence and coin-flipping games
- Unitary Equivalence of Quantum Walks
- Accelerated quantum walk, two-particle entanglement generation and localization
- Invariance in quantum walks with time-dependent coin operators
- Understanding and controlling N-dimensional quantum walks via dispersion relations. Application to the 2D and 3D Grover walks: Diabolical points and more
- Sub-ballistic behaviour of the Quantum Kicked Rotor
- Fractional dynamics in the Lévy quantum kicked rotor
- Anomalous diffusion in the resonant quantum kicked rotor
- Driving the resonant quantum kicked rotor via extended initial conditions
- Invariance in Quantum Walks
- Characterization of anomalous diffusion in one-dimensional quantum walks