{"title":"量子铺路：当球体填料遇到 Gabor 框架","authors":"Markus Faulhuber, Thomas Strohmer","doi":"arxiv-2408.08975","DOIUrl":null,"url":null,"abstract":"We introduce the new problems of quantum packing, quantum covering, and\nquantum paving. These problems arise naturally when considering an algebra of\nnon-commutative operators that is deeply rooted in quantum physics as well as\nin Gabor analysis. Quantum packing and quantum covering show similarities with\nenergy minimization and the dual problem of polarization. Quantum paving, in\nturn, aims to simultaneously optimize both quantum packing and quantum\ncovering. Classical sphere packing and covering hint the optimal configurations\nfor our new problems. We present solutions in certain cases, state several\nconjectures related to quantum paving and discuss some applications.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quantum paving: When sphere packings meet Gabor frames\",\"authors\":\"Markus Faulhuber, Thomas Strohmer\",\"doi\":\"arxiv-2408.08975\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce the new problems of quantum packing, quantum covering, and\\nquantum paving. These problems arise naturally when considering an algebra of\\nnon-commutative operators that is deeply rooted in quantum physics as well as\\nin Gabor analysis. Quantum packing and quantum covering show similarities with\\nenergy minimization and the dual problem of polarization. Quantum paving, in\\nturn, aims to simultaneously optimize both quantum packing and quantum\\ncovering. Classical sphere packing and covering hint the optimal configurations\\nfor our new problems. We present solutions in certain cases, state several\\nconjectures related to quantum paving and discuss some applications.\",\"PeriodicalId\":501114,\"journal\":{\"name\":\"arXiv - MATH - Operator Algebras\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Operator Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.08975\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Operator Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.08975","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Quantum paving: When sphere packings meet Gabor frames
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.
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