Quantum walks;
Quantum simulation;
Lattice field theory;
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摘要:
A quantum walk (QW) simulating the flat (1+2)\documentclass[12pt]{minimal}
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\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}
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\begin{document}$${\mathrm{SO}}(3)$$\end{document}, but rather of its double cover SU(2)\documentclass[12pt]{minimal}
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\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}
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\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.
机构:
Department of Physics, Center for Integrated Plasma Studies, University of Colorado Boulder, Boulder,CO,80309, United StatesDepartment of Physics, Center for Integrated Plasma Studies, University of Colorado Boulder, Boulder,CO,80309, United States
Shi, Yuan
Beck, Kristin M.
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Lawrence Livermore National Laboratory, CA,94550, United StatesDepartment of Physics, Center for Integrated Plasma Studies, University of Colorado Boulder, Boulder,CO,80309, United States
Beck, Kristin M.
Kruse, Veronika Anneliese
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机构:
Lawrence Livermore National Laboratory, CA,94550, United StatesDepartment of Physics, Center for Integrated Plasma Studies, University of Colorado Boulder, Boulder,CO,80309, United States
Kruse, Veronika Anneliese
Libby, Stephen B.
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机构:
Lawrence Livermore National Laboratory, CA,94550, United StatesDepartment of Physics, Center for Integrated Plasma Studies, University of Colorado Boulder, Boulder,CO,80309, United States
机构:
Univ KwaZulu Natal, Sch Chem & Phys, ZA-4000 Durban, South Africa
Inst Math Sci, Ctr Quantum Sci, Madras 600113, Tamil Nadu, IndiaUniv KwaZulu Natal, Sch Chem & Phys, ZA-4000 Durban, South Africa
Goyal, Sandeep K.
Roux, Filippus S.
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CSIR, Natl Laser Ctr, ZA-0001 Pretoria, South AfricaUniv KwaZulu Natal, Sch Chem & Phys, ZA-4000 Durban, South Africa
Roux, Filippus S.
Forbes, Andrew
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Univ KwaZulu Natal, Sch Chem & Phys, ZA-4000 Durban, South Africa
CSIR, Natl Laser Ctr, ZA-0001 Pretoria, South AfricaUniv KwaZulu Natal, Sch Chem & Phys, ZA-4000 Durban, South Africa