Twisted quantum walks, generalised Dirac equation and Fermion doubling

• URL: http://arxiv.org/abs/2212.13859v3
• Date: Mon, 24 Apr 2023 12:53:13 GMT
• Title: Twisted quantum walks, generalised Dirac equation and Fermion doubling
• Authors: Nicolas Jolly and Giuseppe Di Molfetta
• Abstract summary: We introduce a new family of quantum walks, said twisted, which admits as continuous limit, a generalized Dirac operator equipped with a dispersion term. This quadratic term in the energy spectrum acts as an effective mass, leading to a regularization of the well known Fermion doubling problem.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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