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.

中文翻译：

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相对论波包中超振荡的演化

我们分析了相对论波包中超振荡的演化。建立了一个简单的超振荡波包，并根据Klein-Gordon方程和Dirac方程自由演化。超振动各向异性地发展并且在一段时间后衰减。寿命和各向异性都可以通过复杂波数差异很大的分量对波包的贡献的相互作用来理解。该分析得到数值计算的支持，并将结果与​​非相对论分析进行比较。提出了一个潜在的实验，其中可以测量相对论效应对超振荡的重要性。