量子铺砌：当球体堆积遇上Gabor框架
Quantum paving: When sphere packings meet Gabor frames
AI总结：
该研究提出量子堆积、量子覆盖与量子铺砌三类源于非交换算子代数的新问题，类比经典球体堆积与覆盖探索最优构型，给出特定情形的解、相关猜想及应用方向。
摘要：
我们提出了量子堆积、量子覆盖与量子铺砌三类新问题。这些问题在研究一类非交换算子代数时自然涌现，该代数既深深植根于量子物理领域，也与Gabor分析密切相关。量子堆积与量子覆盖问题分别和能量最小化、极化对偶问题存在相似性，而量子铺砌的目标则是同时优化量子堆积与量子覆盖两类问题。经典球体堆积与覆盖问题为这些新问题的最优构型提供了启发。我们给出了若干特定情形下的解，提出了数个与量子铺砌相关的猜想，并讨论了部分应用场景。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
