The Dirac equation as a quantum walk over the honeycomb and triangular lattices
arXiv:1803.01015 · doi:10.1103/PhysRevA.97.062111
Abstract
A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to well-known physics partial differential equations, such as the Dirac equation. We show that these simulation results need not rely on the grid: the Dirac equation in --dimensions can also be simulated, through local unitaries, on the honeycomb or the triangular lattice. The former is of interest in the study of graphene-like materials. The latter, we argue, opens the door for a generalization of the Dirac equation to arbitrary discrete surfaces.
2 figures. Any comments is very welcome! Accepted in PRA
References in corpus (23)
- The electronic properties of graphene
- Massive Dirac fermions in a ferromagnetic kagome metal
- Two-particle bosonic-fermionic quantum walk via 3D integrated photonics
- Exploring Topological Phases With Quantum Walks
- From quantum cellular automata to quantum lattice gases
- Lattice Boltzmann Equation for Quantum Mechanics
- Dirac and Weyl Equations on a Lattice as Quantum Cellular Automata
- Electric quantum walks with individual atoms
- Numerical Solution of the Time-Dependent Dirac Equation in Coordinate Space without Fermion-Doubling
- Quantum Walks in artificial electric and gravitational Fields
- The Dirac equation as a quantum walk: higher dimensions, observational convergence
- Two-component Dirac-like Hamiltonian for generating quantum walk on one-, two- and three-dimensional lattices
- Spinfoam fermions
- Discrete Lorentz covariance for Quantum Walks and Quantum Cellular Automata
- Spatial search in a honeycomb network
- Quantum walks and gravitational waves
- Quantum walks and quantum search on graphene lattices
- Quantum Walks, Weyl equation and the Lorentz group
- Spatial quantum search in a triangular network
- Quantum walk transport properties on graphene structures
- Isotropic quantum walks on lattices and the Weyl equation
- An Effective Hamiltonian Approach to Quantum Random Walk
- Quantum walk on a cylinder
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- Multi-Dimensional Quantum Walks: a Playground of Dirac and Schrödinger Particles
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