Discrete Geometry from Quantum Walks
Keyword(s):
A particular family of Discrete Time Quantum Walks (DTQWs) simulating fermion propagation in 2D curved space-time is revisited. Usual continuous covariant derivatives and spin-connections are generalized into discrete covariant derivatives along the lattice coordinates and discrete connections. The concepts of metrics and 2-beins are also extended to the discrete realm. Two slightly different Riemann curvatures are then defined on the space-time lattice as the curvatures of the discrete spin connection. These two curvatures are closely related and one of them tends at the continuous limit towards the usual, continuous Riemann curvature. A simple example is also worked out in full.
Keyword(s):
2012 ◽
Vol 53
(12)
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pp. 123302
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2013 ◽
Vol 10
(7)
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pp. 1621-1625
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2010 ◽
Vol 77
(4)
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pp. 479-488
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2018 ◽
Vol 29
(10)
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pp. 1850098
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2020 ◽
Vol 315
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pp. 48-58
1979 ◽
Vol 367
(1728)
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pp. 123-141
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Keyword(s):
2009 ◽
Vol 8
(5)
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pp. 387-399
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2016 ◽
Vol 443
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pp. 179-191
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