Dispersive Quantization
Dispersive Quantization
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DOI：
10.4169/000298910x496723
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发表时间：
2010-08-01
影响因子：
0.5
通讯作者：
Olver, Peter J.
中科院分区：
文献类型：
--
作者：
Olver, Peter J.
通过线性色散，分段恒定周期初始数据的演化在合理时间导致令人惊讶的量子化结构，在非理性时间导致分形的不可微剖面。在光学和量子力学中也观察到类似的现象，并与数论中的指数和产生了有趣的联系。这些观测结果对数值和非线性色散的影响被作为开放问题提出。
The evolution, through linear dispersion, of piecewise constant periodic initial data leads to surprising quantized structures at rational times, and fractal, nondifferentiable profiles at irrational times. Similar phenomena have been observed in optics and quantum mechanics, and lead to intriguing connections with exponential sums arising in number theory. Rami-fications of these observations for numerics and nonlinear dispersion are proposed as open problems.