Evolution of Superoscillations in the Dirac Field
Evolution of Superoscillations in the Dirac Field
复制标题
狄拉克场中超级振荡的演化
DOI：
--
复制
发表时间：
2020
影响因子：
1.5
通讯作者：
Giovanni Valente
中科院分区：
文献类型：
--
作者：
F. Colombo;Giovanni Valente
超振荡函数是频带受限的函数，其振荡速度可以快于其最快的傅立叶分量。研究超振荡的演化作为场方程的初始基准需要超位移的概念，它推广了超振荡的概念。本文件具有双重目的。第一个是通过引用量子力学薛定谔方程及其变种，对研究超振荡演化的策略进行了更新和完备的解释。第二个目的是处理相对论量子理论中的狄拉克方程。对Dirac方程超振荡演化的处理可以从Klein-Gordon方程的最新结果中推导出来，但还需要进一步的考虑，这在本文中得到了充分的描述。
Superoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. The study of the evolution of superoscillations as initial datum of field equations requires the notion of supershift, which generalizes the concept of superoscillations. The present paper has a dual purpose. The first one is to give an updated and self-contained explanation of the strategy to study the evolution of superoscillations by referring to the quantum-mechanical Schrödinger equation and its variations. The second purpose is to treat the Dirac equation in relativistic quantum theory. The treatment of the evolution of superoscillations for the Dirac equation can be deduced by recent results on the Klein–Gordon equation, but further additional considerations are in order, which are fully described in this paper.