Massless Dirac Equation from Fibonacci Discrete-Time Quantum Walk
arXiv:1410.4759 · doi:10.1007/s40509-015-0038-6
Abstract
Discrete-time quantum walks can be regarded as quantum dynamical simulators since they can simulate spatially discretized Schrödinger, massive Dirac, and Klein-Gordon equations. Here, two different types of Fibonacci discrete-time quantum walks are studied analytically. The first is the Fibonacci coin sequence with a generalized Hadamard coin and demonstrates six-step periodic dynamics. The other model is assumed to have three- or six-step periodic dynamics with the Fibonacci sequence. We analytically show that these models have ballistic transportation properties and continuous limits identical to those of the massless Dirac equation with coin basis change.
6 pages, 3 figures
References in corpus (12)
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Exploring Topological Phases With Quantum Walks
- Realization of quantum walks with negligible decoherence in waveguide lattices
- Quantum Communication through Spin Chain Dynamics: an Introductory Overview
- A 2D Quantum Walk Simulation of Two-Particle Dynamics
- Discrete single-photon quantum walks with tunable decoherence
- Relationship Between Quantum Walk and Relativistic Quantum Mechanics
- Quantum phase transition using quantum walks in an optical lattice
- Observation of quasiperiodic dynamics in a one-dimensional quantum walk of single photons in space
- Survival probability in a one-dimensional quantum walk on a trapped lattice
- Continuous Limit of Discrete Quantum Walks
- Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality
Cited by in corpus (7)
- Quantum walks with sequential aperiodic jumps
- Genuine Parrondo's paradox in quantum walks with time-dependent coin operators
- Asymptotic properties of the Dirac quantum cellular automaton
- Dirac quantum walks on triangular and honeycomb lattices
- Probing coherence and noise tolerance in discrete-time quantum walks: unveiling self-focusing and breathing dynamics
- Theoretical Studies on Quantum Walks with a Time-varying Coin
- Enhanced spreading in continuous-time quantum walks using aperiodic temporal modulation of defects