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arXiv · 2212.13859

Twisted quantum walks, generalised Dirac equation and Fermion doubling

Nicolas Jolly·Giuseppe Di Molfetta
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Abstract

Quantum discrete-time walkers have, since their introduction, demonstrated applications in algorithmic and in modeling and simulating a wide range of transport phenomena. They have long been considered the discrete-time and discrete space analogue of the Dirac equation and have been used as a primitive to simulate quantum field theories precisely because of some of their internal symmetries. In this paper we introduce a new family of quantum walks, said twisted, which admits, as continuous limit, a generalized Dirac operator equipped with a dispersion term. Moreover, this quadratic term in the energy spectrum acts as an effective mass, leading to a regularization of the well known Fermion doubling problem.

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Nicolas Jolly, Giuseppe Di Molfetta. 2022-12-28. Twisted quantum walks, generalised Dirac equation and Fermion doubling. https://doi.org/10.1140/epjd%2Fs10053-023-00659-9

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