Quantum paving: When sphere packings meet Gabor frames

Markus Faulhuber, Thomas Strohmer
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Abstract

We introduce the new problems of quantum packing, quantum covering, and quantum paving. These problems arise naturally when considering an algebra of non-commutative operators that is deeply rooted in quantum physics as well as in Gabor analysis. Quantum packing and quantum covering show similarities with energy minimization and the dual problem of polarization. Quantum paving, in turn, aims to simultaneously optimize both quantum packing and quantum covering. Classical sphere packing and covering hint the optimal configurations for our new problems. We present solutions in certain cases, state several conjectures related to quantum paving and discuss some applications.
量子铺路:当球体填料遇到 Gabor 框架
我们介绍了量子堆积、量子覆盖和量子铺垫等新问题。这些问题是在考虑非交换算子代数时自然产生的,它深深植根于量子物理和 Gabor 分析。量子堆积和量子覆盖与能量最小化和极化的对偶问题有相似之处。量子铺层的目的是同时优化量子堆积和量子覆盖。经典的球体堆积和覆盖为我们的新问题提示了最优配置。我们提出了某些情况下的解决方案,阐述了与量子铺层相关的几个猜想,并讨论了一些应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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