Discrete time Dirac quantum walk in 3+1 dimensions
arXiv:1603.06442 · doi:10.3390/e18060228
Abstract
In this paper we consider quantum walks whose evolution converges to the Dirac equation one in the limit of small wave-vectors. We show exact Fast Fourier implementation of the Dirac quantum walks in one, two and three space dimensions. The behaviour of particle states, defined as states smoothly peaked in some wave-vector eigenstate of the walk, is described by an approximated dispersive differential equation that for small wave-vectors gives the usual Dirac particle and antiparticle kinematics. The accuracy of the approximation is provided in terms of a lower bound on the fidelity between the exactly evolved state and the approximated one. The jittering of the position operator expectation value for states having both a particle and an antiparticle component is analytically derived and observed in the numerical implementations.
17 pages, 13 figures. D'Ariano, G.M.; Mosco, N.; Perinotti, P.; Tosini, A. Discrete Time Dirac Quantum Walk in 3+1 Dimensions. Entropy 2016, 18, 228
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