Evolution of superoscillations in a relativistic wavepacket

We analyse the evolution of superoscillations in a relativistic wavepacket. A simple superoscillating wavepacket is set up and is allowed to evolve freely according to both the Klein-Gordon equation and the Dirac equation. The superoscillations evolve anisotropically and decay after a time. Both the...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2020-05, Vol.53 (17), p.175302
Main Authors: Herklots, J R, Strange, P
Format: Article
Language:English
Subjects:
Dirac equation
Klein-Gordon equation
superoscillations
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Summary:We analyse the evolution of superoscillations in a relativistic wavepacket. A simple superoscillating wavepacket is set up and is allowed to evolve freely according to both the Klein-Gordon equation and the Dirac equation. The superoscillations evolve anisotropically and decay after a time. Both the lifetime and anisotropy can be understood in terms of the interaction of contributions to the wavepacket from components with strongly differing complex wavenumber. The analysis is supported by numerical calculations and the results are compared with the non-relativistic analysis. A potential experiment in which the significance of relativistic effects on superoscillations could be measured is proposed.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ab7d5f