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Relativistic effects and rigorous limits for discrete- and continuous-time quantum walks
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10.1063/1.2759837
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Affiliations:
1 National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8423
a) Electronic mail: frederick.strauch@nist.gov
J. Math. Phys. 48, 082102 (2007)
/content/aip/journal/jmp/48/8/10.1063/1.2759837
http://aip.metastore.ingenta.com/content/aip/journal/jmp/48/8/10.1063/1.2759837
View: Figures

## Figures

FIG. 1.

Probability distribution of the Dirac wave packet with and for values of the localization parameter: (a) , (b) , and (c) .

FIG. 2.

Probability distribution of the Dirac wave packet with and for values of the spinor components: (a) , (b) , and (c) .

FIG. 3.

Moments of the Dirac wave packet, with and , as a function of : (a) , (b) , (c) , and (d) . The solid curves are the exact moments, while the dashed curves are the and asymptotic expressions. Note that the scale is logarithmic in , and that in (c) we have isolated the ratio .

FIG. 4.

Probability distribution of the DTQW wave packet with and for values of the localization parameter: (a) , (b) , and (c) .

FIG. 5.

Probability distribution of the DTQW wave packet with and for values of the coin parameter: (a) , (b) , and (c) . Note that each time axis has been chosen such that the final time satisfies .

FIG. 6.

Moments of the DTQW wave packet, with and , as a function of : (a) , (b) , (c) , and (d) . The solid curves are the exact moments, while the dashed curves are the and asymptotic expressions. Note that the scale is logarithmic in .

FIG. 7.

Probability distribution of (a) the DTQW wave packet with and , (b) the Bessel function approximation to the DTQW with and , and (c) the CTQW with and .

FIG. 8.

Entanglement of the Dirac wave function as a function of , for various values of . Note that the label (1,1,1) actually refers to .

FIG. 9.

Entanglement of the Dirac wave function as a function of (see text), for (a) , (b) , and (c) . Note that the axes have been rotated to show the region near .

FIG. 10.

Entanglement of the DTQW wave function with as a function of , for various values of . Note that the label (1,1,1) actually refers to .

FIG. 11.

Entanglement of the DTQW wave function as a function of (see text), for (a) , (b) , and (c) . Note that the axes have been rotated to show the region near .

FIG. 12.

Entanglement of the DTQW wave function as a function of (see text), for and (a) , (b) , and (c) .

FIG. 13.

Probability distribution of the Dirac wave packet with , for (a) , (b) , and (c) .

FIG. 14.

Probability distribution of the DTQW wave packet with and for values of the localization parameter: (a) , (b) , and (c) .

FIG. 15.

Probability distribution of the DTQW wave packet with and for values of the coin parameter: (a) , (b) , and (c) . Note that each time axis has been chosen such that the final time satisfies .

/content/aip/journal/jmp/48/8/10.1063/1.2759837
2007-08-02
2014-04-17

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