Dirac quantum walks with conserved angular momentum

被引:0
|
作者
Gareth Jay
Pablo Arnault
Fabrice Debbasch
机构
[1] The University of Western Australia,Physics Department
[2] Universidad de Valencia and CSIC,Departamento de Física Teórica and IFIC
[3] Institute for Quantum Computing,Laboratoire de Recherche sur les Sciences de la Matiére (LARSIM)
[4] IRFU,undefined
[5] Sorbonne Université,undefined
[6] Observatoire de Paris,undefined
[7] Université PSL,undefined
[8] CNRS,undefined
[9] LERMA,undefined
关键词
Quantum walks; Quantum simulation; Lattice field theory;
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学科分类号
摘要
A quantum walk (QW) simulating the flat (1+2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(1 + 2)$$\end{document}D Dirac equation on a spatial polar grid is constructed. Because fermions are represented by spinors, which do not constitute a representation of the rotation group SO(3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{SO}}(3)$$\end{document}, but rather of its double cover SU(2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{SU}}(2)$$\end{document}, the QW can only be defined globally on an extended spacetime where the polar angle extends from 0 to 4π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4 \pi $$\end{document}. The coupling of the QW with arbitrary electromagnetic fields is also presented. Finally, the cylindrical relativistic Landau levels of the Dirac equation are computed explicitly and simulated by the QW.
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页码:419 / 430
页数:11
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