Evolution of superoscillations for Schrödinger equation in a uniform magnetic field
Evolution of superoscillations for Schrödinger equation in a uniform magnetic field
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均匀磁场中薛定谔方程超振荡的演化
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
D. Struppa
中科院分区：
文献类型：
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作者：
F. Colombo;J. Gantner;D. Struppa
Aharonov-Berry超振荡是带限函数，其振荡速度比其最快傅立叶分量快。超振荡出现在科学和技术的几个领域，如阿哈罗诺夫在量子力学，光学和信号处理中的弱测量。利用薛定谔方程研究弱初值条件下超振荡的演化是一个重要的问题。一些超振荡函数不是平方可积的，但它们是真实的解析函数，可以推广到整全纯函数。这一事实导致了一类卷积算子的连续性的研究，适当的空间的整个功能的增长条件。本文研究了均匀磁场中超振荡初始数据的演化。此外，我们收集了一些结果卷积算子出现在理论的超振荡函数使用直接的方法，允许卷积算子有非…
Aharonov-Berry superoscillations are band-limited functions that oscillate faster than their fastest Fourier component. Superoscillations appear in several fields of science and technology, such as Aharonov’s weak measurement in quantum mechanics, in optics, and in signal processing. An important issue is the study of the evolution of superoscillations using the Schrodinger equation when the initial datum is a weak value. Some superoscillatory functions are not square integrable, but they are real analytic functions that can be extended to entire holomorphic functions. This fact leads to the study of the continuity of a class of convolution operators acting on suitable spaces of entire functions with growth conditions. In this paper, we study the evolution of a superoscillatory initial datum in a uniform magnetic field. Moreover, we collect some results on convolution operators that appear in the theory of superoscillatory functions using a direct approach that allows the convolution operators to have non...