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• W2260162774 abstract "A particular example is produced to prove that quantum walks can be used to simulate full-fledged discrete gauge theories. A family of two-dimensional walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac fermion coupled to arbitrary electromagnetic fields. The electromagnetic interpretation is extended beyond the continuous limit by proving that these discrete-time quantum walks (DTQWs) exhibit an exact discrete local U(1) gauge invariance and possess a discrete gauge-invariant conserved current. A discrete gauge-invariant electromagnetic field is also constructed and that field is coupled to the conserved current by a discrete generalization of Maxwell equations. The dynamics of the DTQWs under crossed electric and magnetic fields is finally explored outside the continuous limit by numerical simulations. Bloch oscillations and the so-called $mathbf{E}ifmmodetimeselsetexttimesfi{}mathbf{B}$ drift are recovered in the weak-field limit. Localization is observed for some values of the gauge fields." @default.
• W2260162774 created "2016-06-24" @default.
• W2260162774 creator A5029249407 @default.
• W2260162774 creator A5035578344 @default.
• W2260162774 date "2016-05-02" @default.
• W2260162774 modified "2023-09-26" @default.
• W2260162774 title "Quantum walks and discrete gauge theories" @default.
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• W2260162774 doi "https://doi.org/10.1103/physreva.93.052301" @default.
• W2260162774 hasPublicationYear "2016" @default.
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