Next Article in Journal
Information and Selforganization: A Unifying Approach and Applications
Next Article in Special Issue
Entropy? Honest!
Previous Article in Journal
Fractional-Order Grey Prediction Method for Non-Equidistant Sequences
Previous Article in Special Issue
Quantum Errors and Disturbances: Response to Busch, Lahti and Werner
Open AccessArticle

Discrete Time Dirac Quantum Walk in 3+1 Dimensions

QUIT group, Dipartimento di Fisica, via Bassi 6, Pavia 27100, Italy
INFN Gruppo IV, Sezione di Pavia, via Bassi 6, Pavia 27100, Italy
Author to whom correspondence should be addressed.
Academic Editors: Gregg Jaeger and Andrei Khrennikov
Entropy 2016, 18(6), 228;
Received: 4 March 2016 / Revised: 28 May 2016 / Accepted: 30 May 2016 / Published: 14 June 2016
In this paper we consider quantum walks whose evolution converges to the Dirac equation 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. View Full-Text
Keywords: quantum walk; Dirac equation quantum walk; Dirac equation
Show Figures

Graphical abstract

MDPI and ACS Style

D’Ariano, G.M.; Mosco, N.; Perinotti, P.; Tosini, A. Discrete Time Dirac Quantum Walk in 3+1 Dimensions. Entropy 2016, 18, 228.

AMA Style

D’Ariano GM, Mosco N, Perinotti P, Tosini A. Discrete Time Dirac Quantum Walk in 3+1 Dimensions. Entropy. 2016; 18(6):228.

Chicago/Turabian Style

D’Ariano, Giacomo M.; Mosco, Nicola; Perinotti, Paolo; Tosini, Alessandro. 2016. "Discrete Time Dirac Quantum Walk in 3+1 Dimensions" Entropy 18, no. 6: 228.

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

Search more from Scilit
Back to TopTop