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Preprints, Working Papers, ... Year : 2018

Dirac equation as a quantum walk over the honeycomb and triangular lattices

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 (2+1)–dimensions can also be simulated, through local unitaries, on the honeycomb or the triangular lattice, both of interest in the study of quantum propagation on the non-rectangular grids, as in graphene-like materials. The latter, in particular, we argue, opens the door for a generalization of the Dirac equation to arbitrary discrete surfaces.
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Dates and versions

hal-03594743 , version 1 (05-09-2023)

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Pablo Arrighi, Di Molfetta Giuseppe, Iván Márquez-Martín, Armando Pérez. Dirac equation as a quantum walk over the honeycomb and triangular lattices. 2023. ⟨hal-03594743⟩
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